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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
Two.
∙It will be spun on a number less than 10 in 75 times if you spin it 100 times.
Explanation:
Let x be the random variable, x = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
The probability for any outcome is P(x) = 1/12. It is a flat probability distribution.
The probability that when you spin the spinner the outcome is a number greater than
10 is:
P(10 ≤ x ≤ 12) = P(x = 10) + P(x = 11) + P(x = 12 ) = 3/12 = 1/4
The probability of the complement event (that the outcome is a number smaller than 10) is: P(x < 10) = 1 - 1/4 = 3/4.
So the expected number of times the spinner outcome will be a number smaller than 10 is:
P(No. outcomes x<10 in 100 spins) = 100 ∙ P(x<10) = 100 ∙ 3/4 = 75
Two coins are flipped and a die is rolled how many possible outcomes are there?
Each coin can land in two ways.
The die has 6 possible outcomes.
So there are 2 x 2 x 6 = 24 possible outcomes for the whole experiment.
Note that I am assuming the coins can be told apart - say the first coin and 2nd coin and that H and then T is different that T and then H. If not, then there are only be three outcomes for the coins-- 2 heads, 1 head or no heads and the total number of outcomes would be 3 X 6 = 18.
Do your clothes get less wrinkled if you roll them?
They will get more wrinkled if you roll them. When you roll them they bend, creating folds and, if stored long enough, the folds will become wrinkles. The best way to keep clothes from getting wrinkled is laying them flat, not folding or anything. However this takes up alot of room so it would be best to fold them.
Theoretical
Empirical
What is the theoretical probability of rolling a factor of 6 on a die?
When rolling a die, a 1, or a 2, or a 3, or a 4, or a 5, or a 6 will come up. Factors of six are 1, 2, 3 and 6. This leaves 4 and 5 that are not factors of 6. The probability of rolling any one number in one roll of the die is 1 in 6, or 1/6. To find a "cumulative" probability where we "combine" the odds of rolling several numbers, as is the case here, we simply add the probability of rolling each number together and sum them.
In the case here, the probability of rolling 1 is 1/6, and the probability of rolling 2 is also 1/6, and the probability of rolling 3 is 1/6 and the probability of rolloing 6 is 1/6. We add 1/6 + 1/6 + 1/6 + 1/6 and get 1+1+1+1/6, which is 4/6. The 4/6 reduces to 2/3, and that 2/3 represents the probability of rolling a factor of 6 with one roll of a die. There is one more little thing.
Probability is a mathematical term where "odds" are expressed on a scale of zero (0) to one (1). The probability of something happening is either 0, or 1, or something in between. If the probability of something happening is 100% (which is to say that somehting must occur), then the probability is 1. And if something cannot happen, then the probability of it occurring is 0. In this light, the 2/3 chance of rolling a factor of 6 with one roll of a die is 0.6666....
If you roll a dice twice what is the theoretical probability of rolling three then four?
On a normal 6 sided dice the probability of rolling any number is 1/6.
When we want a 3 AND then a 4 we multiply the probabilities together.
So P(3 then 4) = 1/6 x 1/6 = 1/36
What are the possible outcomes for flipping 2 coins?
HH, HT, TH, or TT. Each has a probability of 1/4. You might consider HT and TH the same, in which case you'd say the probably of HH and TT are 1/4 each and the probability of TH is 1/2.
Addition rule for probability of events A and B?
If they're disjoint events:
P(A and B) = P(A) + P(B)
Generally:
P(A and B) = P(A) + P(B) - P(A|B)
3 pictures are selected randomly from 5 pictures and arrange how many ways are there to arrange?
Assuming the question is that you have 5 pictures and want to know how many different ways you could put 3 on a wall from left to right:
There are 5 choices for the first picture; for each of these there are 4 choices for the second; and for each of these choices there are 3 choices for the third, meaning a total of:
5 x 4 x 3 = 60 ways that 3 pictures can be arranged from 5.
The probability is the number of girls divided by the number of students, so 12/22, or 6/11
64/256
One-way independence.
The z score for the mean is always 0.
If you flip a coin 5 times what is the probability that the coin will land on heads all five times?
The probability that the coin lands on the heads ones: 1/2
Two times (1/2)^2 = 1/4
Five times (1/2)^5 = 1/32 (so 1 in 32 attempts)
n times (1/2)^n
What is an event that occurs because of a preceding event?
A dependent event. Or rather, a dependent event is one whose probability of occurrence is affected by previous events. For instance, drawing a card from a deck is affected by previous draws, if there's no replacement.
Sample space of tossing a coin 6 times?
{hhhhhh, hhhhht, hhhhth, hhhhtt, hhhthh, hhhtht, hhhtth, hhhttt, hhthhh, hhthht, hhthth, hhthtt, hhtthh, hhttht, hhttth, hhtttt, hthhhh, hthhht, hthhth, hthhtt, hththh, hththt, hthtth, hthttt, htthhh, htthht, htthth, htthtt, httthh, htttht, htttth, httttt, thhhhh, thhhht, thhhth, thhhtt, thhthh, thhtht, thhtth, thhttt, ththhh, ththht, ththth, ththtt, thtthh, thttht, thttth, thtttt, tthhhh, tthhht, tthhth, tthhtt, tththh, tththt, tthtth, tthttt, ttthhh, ttthht, ttthth, ttthtt, tttthh, ttttht, ttttth, tttttt}
Edit: It removed all my capitalization, but everything should be capitalized.
This problem doesn't lead to a whole number solution. Are you sure you copied it correctly? Maybe you meant the ratio is 4 to 3. In that case:
red/blue = 4/3
blue/red = 3/4
blue = (3 * red) / 4 = (3 * 16) / 4 = 12 blue marbles
Number of useful outcomes over number of possible outcomes and simplify it if you can. Imagine you want an even number and you roll a die. There are 6 possible outcomes and three of them are useful outcomes (outcomes we want).
3
6
Simplify it and you get
1
2
