# Conditional probability, combinations, permutations

Find the number of possible combinations of picking 2 items out of 6.

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How many permutations of answers are possible in a true-false test consisting of 10 questions?

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A meeting is to be addressed by 5 speakers, A, B, C, D, and E. In how many ways can the speakers be ordered if B must not follow A?

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Calculate the probability of a number card (A, 2, 3, 4, 5, 6, 7, 8, 9, 10) being drawn from a deck of cards

The Chicago Blackhawks hockey team has a probability of winning of 0.6 and a probability of losing of 0.25. What is the probability of a tie?

It has been estimated that in 70% of fatal accidents involving two cars, at least one of the drivers is drunk. If you hear of a two-car fatal accident, what odds should you give a friend for the event that at least one of the drivers was drunk?

For a 3-child family, find the probability of exactly 1 girl, given that the first child is a boy.

If 2 cards are drawn from a regular deck of 52 cards without replacement, what is the probability that the second card is a queen? (Note: your final answer must be a single probability)

A pair of fair dice is thrown 3 times. What is the probability that on the first toss the sum of the 2 dice is even, on the second toss the sum is less than 6, and on the third toss the sum is 7? (Note: your final answer must be a single probability)

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#### Solution Preview

Let C(n,m)=n!/(m!*(n-m)!), P(n,m)=n!/(n-m)!

Find the number of possible combinations of picking 2 items out of 6.

Answer: C(6,2)=15

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How many permutations of answers are possible in a true-false test consisting of 10 questions?

Answer: 2^10=1024

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A meeting is to be addressed by 5 speakers, A, B, C, D, and E. In how many ways can the speakers be ordered if B must not follow A?

Answer: 5!/2=60

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Calculate the probability of a number card (A, 2, 3, 4, 5, 6, ...

#### Solution Summary

This is a series of questions regarding permutations, combinations, and conditional probability.