Probability

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.

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%

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!

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.

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."

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!

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).

Ah, what a lovely question! It's actually "heads of state" when referring to the leaders of different countries. Remember, when we talk about multiple leaders, we keep "state" singular to show they are all part of the same concept. Keep painting with those words, my friend!

Oh, dude, the probability of guessing the last digit of a phone number is 1 in 10, because there are 10 possible digits (0-9). So, like, if you randomly guess, you have a 10% chance of getting it right. But hey, don't stress about it too much, it's just a phone number!

50%

Two coins tossed sample space is (H=Heads, T = Tails) as follows. HH, HT, TH, TT is the sample space.

Generally people who act and treat others well are treated well by others.
That is not to say that good things happen to them more than people who are less pleasant. Misfortune happens to the good, bad and the indifferent in equal measure. As does good fortune.

A matched test is appropriate only if the two variables are measures taken for the same subject.

6x6x6=216

Yes.

1/2

2 out of 12

This is going to be big. To simplify the idea some, start with the digit, and write Even & Odd. The even side will look exactly like the odd side. Then for the first letter, list all 26 letters. Then under each letter, list all 26 letters again. So under ODD you will have 676 letters. And the same under Even, for 1352. Looking at the odd side, you have the first tier P has 26 under it, and Q has 26 under it for 52. Then for the other 24 letters, each one has 2 'winners', so 48 more. So there are 100 winners out of 1352 total.

A lot of people have a difficult time getting over the red walls. This seems to mostly affect people on slower computers since timing is critical, and at slow frame rates it is hard to do the jump. The best way to get over these walls is to simply jump on top of one of the wooden blocks. Then jump again and start flying at the apex of the jump. You should now be able to just flyover the red wall.Many people have a hard time finding the marble. The passage to the marble is narrow, but there is a line of acorns marking the entrance. Just keep going to the end of the passage and the marble will be there.The correct way to do the marble bowling is to drop the marble and kick it into the batteries, however, you can also get a running start and just drop the marble. That will send it coasting into the batteries too, and this method is often more accurate than kicking.The slot car racing is really a no-brainer. Just hold down the throttle until the race is over - you'll win every time.

The answer depends on how many of the 5 cards are similar.

The probability of rolling a 4 is 3/36 .

The propbability of rolling 12 is 1/36 .

The probability of rolling either one is 4/36 = 1/9 = 111/9 percent.

We have to use the expression P(X=x) = nCx px (1--p)(n--x)

Here n = n and p=p and x = 1 or x>1

P(X>/=1) = 1 -- P(X</=1)

So, P(X<=1) = P(X=0) + P(X=1)

This gives nC0 p0 (1--p)(n-0)+ nC1 p1 (1--p)(n--1)

ie (1--p)n + n p (1--p)(n--1)

Bimodal Distribution

The probability of any one number on a die being rolled is 1/6 or 16.67%.