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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
How ways cam you arrange a 4 letter word Adam?
If you have 4 DIFFERENT letters, there are 24 ways - this is equal to 4! (that is, the factorial of 4). Because of the two repeated letters, if you do this, you get every valid combination repeated twice (i.e., by exchanging one "a" with the other "a" you get an identical combination). Therefore the real number of arrangements is only one-half that value.
How many red 2's are in a deck of cards?
A standard deck of cards contains 52 cards, which includes 4 suits - hearts, diamonds, clubs, and spades. Each suit has one red 2, specifically the 2 of hearts and the 2 of diamonds. Therefore, there are two red 2's in a deck of cards.
Well, honey, if 80% of California drivers wear seat belts, then the probability of one driver wearing a seat belt is 0.8. So, the probability of all three drivers wearing their seat belts would be 0.8 x 0.8 x 0.8, which equals 0.512 or 51.2%. So, there you have it, buckle up and enjoy the ride!
What are the chances of rolling doubles 7 times in a row?
The probability of rolling doubles on a fair six-sided die is 1/6. To roll doubles 7 times in a row, you would need to multiply this probability by itself 7 times, resulting in (1/6)^7. This equals approximately 1 in 78,364,164,096, which means the chances of rolling doubles 7 times in a row are extremely low.
What is the probability of getting an ace or a joker from a pack of 54 cards?
Well, isn't that a happy little question! In a pack of 54 cards with 2 jokers, you have 4 aces and 2 jokers. So, you have a total of 6 cards that are either aces or jokers. To find the probability, you simply divide the number of favorable outcomes (6) by the total number of outcomes (54). So, the probability of drawing an ace or a joker is 6/54, which simplifies to 1/9. Happy painting!
How do you make a maths working model on triangles for school exhibition of class 9th?
Oh, what a delightful project to work on! To make a math working model on triangles for your school exhibition, you can start by gathering materials like cardboard, markers, and a ruler. Then, you can create different types of triangles such as equilateral, isosceles, and scalene using the materials. Remember to label each triangle and showcase their unique properties to help your classmates understand them better. Just remember, there are no mistakes in art or math - only happy little accidents!
What is the probability of drawing 2 hearts in a deck of cards?
The probability of drawing the two of hearts is 1/52.
The probability of drawing two cards that are hearts depends on whether or not the first card is replaced.
If it is replaced, then the probability is (1/4)*(1/4) = 1/16 = 0.0625
while if it is not, the probability is (1/4)*(12/51) = 3/51 = 0.0588 (approx).
Pam is playing with red and black marbles?
Well, isn't Pam just living life on the edge with those red and black marbles? I hope she's not planning on starting a game of roulette anytime soon. Just be careful, Pam, those marbles can be a slippery slope to a high-stakes game of chance.
How many possible outcomes if you toss a coin four times?
- all heads
- all tails
- 3 heads 1 tail
- 3 tails and 1 head
- 2h and 2t
i think only 5 but that's just what i can get
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The above answer is correct if you disregard the order of the outcomes.
If the order of the outcomes matters, then the answer is:
2 x 2 x 2 x 2 = 16
since each toss has two possible outcomes (assuming the coin cannot land on its side) and you repeat the toss four times.
There are 84 different combinations possible for the committee of 6, taken from
4 students and 5 teachers.
1.- The committee with 4 students has 4C4 number of combinations of 4 students out of 4 and 5C2 number of combinations of 2 teachers out of 5 to be combined with. The product of these two give the number of different combinations possible in a committee formed by 4 students and 2 teachers.
2.- The committee with 3 students has 4C3 number of combinations of 3 students out of 4 and 5C3 number of combinations of 3 teachers out of 5 to be combined with. The product of these two give the number of different combinations possible in a committee formed by 3 students and 6 teachers.
3.- The committee with 2 students has 4C2 number of combinations of 2 students
out of 4 and 5C4 number of combinations of 4 teachers out of 5 to be combined with. The product of these two give the number of different combinations possible in a committee formed by 2 students and 4 teachers.
4.- The committee with 1 student has 4C1 number of combinations of 1 student out of 4 students and 5C5 number of combinations of 5 teachers out of 5 to be combined with. The product of these two give the number of different combinations possible in a committee formed by 1 student and 5 teachers.
We now add up all possible combinations:
4C4∙5C2 + 4C3∙5C3 + 4C2∙5C4 + 4C1∙5C5 = 1(10) + 4(10) +6(5) + 4(1) = 84
There are 84 different combinations possible for the committee of 6, taken from
4 students and 5 teachers.
[ nCr = n!/(r!(n-r)!) ]
[ n! = n(n-1)(n-2)∙∙∙(3)(2)(1) ]
What is the experimental probability of rolling a 2 on a number cube rolled 50 times?
Conduct the following experiment:
Roll a number cube 50 times.
Count the number of times you roll a 2.
Divide that number by 50.
That is the experimental probability.
The answer that I might get may well be different to yours. And if you do you experiment another time, the answer is likely to be different.
To create five numbers that are multiples of 5 using the ten cards numbered 0 to 9, you can arrange them as follows:
- Use the cards 0, 5, 6, 7, and 8 to form the number 5,687 (multiple of 5).
- Use the cards 0, 1, 2, 5, and 9 to form the number 9,521 (multiple of 5).
- Use the cards 0, 3, 4, 5, and 8 to form the number 8,543 (multiple of 5).
- Use the cards 0, 2, 5, 6, and 7 to form the number 7,652 (multiple of 5).
- Use the cards 0, 1, 4, 5, and 9 to form the number 9,541 (multiple of 5).
What is the probability to choose a prime number from numbers 1 to 50?
Well, honey, there are 15 prime numbers between 1 and 50. So, the probability of choosing a prime number from that range would be 15 (prime numbers) divided by 50 (total numbers), which simplifies to 3/10 or 30%. Math doesn't have to be boring, darling!
The chance of receiving a blue result is 2 in 4, in other words 50%.
Well, honey, there are 11 marbles in total, and 4 of them are blue. So, if you don't want a blue marble, that leaves you with 7 marbles to choose from. The probability of picking a marble that is not blue is 7/11. Hope that helps, sugar!
Oh, what a lovely scenario we have here! If we imagine each student as a unique color on our palette, we can see that there are 12 different combinations for the order of the speeches. Since we want Joey to be first, Chloe to be second, and Zoe to be third, there is only 1 specific way this can happen. So, the probability is simply 1 out of the 12 possible combinations, which is 1/12. Just like painting a happy little tree, sometimes things come together beautifully in the end.
What would the probability be of drawing 4 hearts out of a deck of 52 cards?
That would depend on how many cards you drew and whether you re-inserted the cards drew back into the deck before re-drawing. I'll list a few examples.
Say you drew:
- 4 cards without re-inserting the cards you drew earlier back into the deck
The probability of drawing 4 hearts would thus be: 13/52 * 12/51 * 11/50 * 10/49 = 0.00264 or 0.264%.
- 4 cards but this time you re-insert the cards you drew earlier back into the deck
The probability of drawing 4 hearts would thus be: 13/52 * 13/52 * 13/52 * 13/52 = (13/52)^4 = 0.00391 or 0.391%
If you roll a die 60 times about how many times will you expect to get 1?
Well, statistically speaking, if you roll a fair six-sided die 60 times, you can expect to get a 1 about 10 times. But hey, don't get too attached to that number, probability can be a fickle friend. Just roll the dice and see what Lady Luck has in store for you!
What number comes next in this sequence 4 6 3 7 9 6 10?
Well, isn't that a fun little sequence we have here! Let's take a moment to appreciate the numbers dancing together. If we look closely, we can see that the pattern alternates between adding 2 and subtracting 3. So, following this pattern, the next number would be 7.
To determine the total number of different types of homes available, you would multiply the number of choices for each category. In this case, you would multiply the 6 basic plans by the 3 roof styles and then by the 2 exterior finishes. Therefore, there would be a total of 6 x 3 x 2 = 36 different types of homes available.
How many ways can you rearrange the letters in the word pencil?
To calculate the number of ways the letters in the word "pencil" can be rearranged, we first determine the total number of letters, which is 6. Since there are two repeated letters (the letter 'e'), we divide the total number of letters by the factorial of the number of times each repeated letter appears. This gives us 6! / 2! = 360 ways to rearrange the letters in the word "pencil."
How many people have the same name and birthday as you?
The first thing to note is that names and birthdays are independent of each other. Someone born on 5th June isn't more likely to be called Chris, and someone called Katie isn't more likely to be born on 20th October, or whatever.
Thus the probability is equal to the probability someone has your name, multiplied by the probability someone has your birthday.
The latter is just 1/365.25, as you are equally likely to be born on each day.
The former could be anything. If you have a really common name, that 1 in 1,000 people have, then the probability of someone having the same birthday and name as you will be 1/365,250
Multiply this probability by the world population (which we'll round to 7 billion) and you get:
7,000,000,000/365,250
= 19,165
so 19,165 people would have the same name and birthday as you!
What is the probability of rolling a composite number with one roll of a die?
A composte number is any number that is not prime.
The numbers 1, 2, 3, 4, 5 and 6 appear on a die.
2, 3 and 5 are prime numbers; and one 1 is niether prime nor composite (unit).
Therefore, 4 and 6 are composite. So the probability or rolling a composite number is 1/3 (2/6).
