probability

You throw two dice. The red dice is fair but on the blue dice the probability of a 1=15%, probability of a 2 is 25%, and the probability of any other number is 15%. What is the probability of getting 4? Possible Rolls with a sum of 4: R = 1, B = 3 R = 2, B = 2 R = 3, B = 1 Probabilities: R =...

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green? We are drawing without...

In a family of 4 children, what is the probability that all four will be girls? P(G) = 1/2 or 0.5 Since each child is independent, we have: 1/2 * 1/2 * 1/2 * 1/2 or (1/2)^4 1/16 or in decimal form, 0.0625

A high school with 1000 students offers two foreign language courses : French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student...

A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement. please show the steps. (a) The first two apples are green. What is the probability that the third apple is red? (b) What is the probability that exactly two of the...

A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colours? The key phrase here is without replacement. First, it's easier to find the probability of both colors...

If 13,754 people voted for a politician in his first election, 15,420 voted for him in his second election, and 8,032 voted for him in the first and second elections, how many people voted for this politician in the first or second election? Let P(A) be the first election votes, P(B) be the...

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same color. Total number of marbles in the bag is 3 + 4 = 7. The problem asks for the...

If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)? P(1) on first roll and P(anything on second roll) = 1/6 * 1 = 1/6 P(anything on first roll) and P(1) on second roll = 1 * 1/6 = 1/6 Add those together...

Jennie and Alex both wanted to get a free ticket for a College Music concert. However, the concert staff told them the tickets were limited. Twenty people wanted to attend the concert but only 10 free tickets were left. So the concert center staff decided to use a lottery to decide who would...

The singular form of the word "dice" is "die". Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What's the probability of getting a three at the third time? Since all trials are independent: 1/6 * 1/6 * 1/6 = 1/216

How many ways can you rolls two dice and get a sum less than 4? Answer is 1/12 using our 2 dice calculator.

Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the probability that the numbers on the balls are consecutive. Build our sample set: (1, 2) (2, 3) (3, 4) (4, 5) (5, 6) (6, 7) (7, 8) (8, 9) (9, 10) Each of these 9 possibilities has a probability of...

2 dice are rolled what is the probability that doubles are rolled less than 11 List out the doubles with a sum less than 11: (1, 1) (2, 2) (3, 3) (4, 4) (5, 5) The probability of each double is 1/6 * 1/6 = 1/36. We have 5 of them, so we have 5*1/36 = 5/36

Since each event is independent, we have: P(T) * P(T) * P(T) 1/2 * 1/2 * 1/2 1/8

Use our 2 dice calculator, you have 2 ways to roll an 11 (5, 6) --> P(5, 6) = 1/36 (6, 5)--> P(6, 5) = 1/36 We want P(5, 6) + P(6, 5): P(5, 6) + P(6, 5) = 1/36 + 1/36 P(5, 6) + P(6, 5) = 2/36 P(5, 6) + P(6, 5) = 1/18

The only way you can roll a 12 with two dice is 6 and 6. Since each die roll is independent, we have: P(12) = P(6) * P(6) P(12) = 1/6 * 1/6 P(12) = 1/36. Now, what is the probability we roll a 12 five times in a row? The same rules apply, each new roll is independent of the last, so we...

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal with µ=8.1 ounces and σ=0.1 ounces. A sample of 5 of these chocolate bars is selected. What is the probability that their average weight is less than 8 ounces? Calculate Z score and probability...

P(X = 4) AND P(X is odd) Which means P(X = 1) + P(X = 3) P(X = 1) = 1/6 P(X = 3) = 1/6 P(X = 1) + P(X = 3) = 1/6 + 1/6 = 2/6 = 1/3

two unbiased dice are thrown. find the probability that the total number on the dice is greater than 10 From our 2 dice calculator: We have (5,6),(6,5),(6,6) P(Sum) > 10 is 1/12