# Statistics examples: Basic probability

* denotes question which is meant for discussion on that stats
forum, so no worked solution is given

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**Question BP001**

*(adapted from LSE paper)*A problem on dice.

(a) If 2 fair dice are thrown, find the probability that the sum of upturned faces is 12.

(b) If 2 fair dice are thrown, find the probability that the sum of upturned faces is 11

*(c) If 3 fair dice are thrown, find the probability the sum of their upturned faces is 12. [Answer is 0.1157]

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### Question BP002

Three athletes, let's label them A,B,C, run a race. They are equally matched. If the 3 race against each other,

(a) find the probability that A wins the race

(b) if you are told A beat C, what is the probability that A won the race?

### Question BP003

Consider 3 events A and B with: P(A) = 0.2, P(B)=0.7, and P(A|B) = 0.3. Find the probabilities that

(a) both events occur

(b) at least one of the events occurs

*(c) exactly one of the events occurs

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### Question BP004

Consider 2 events A and B with P(A)=0.4 and P(A U B) = 0.8. Find

(a) P(A^{c}∩B)

(b) P(B) if A and B are mutually exclusive

*(c) P(B) if A and B are mutually independent

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### Question BP005

Suppose that for married couples to vote in an election, the probability that a husband will vote is 0.7, the probability a wife will vote is 0.5, and the probability a wife votes given her husband votes is 0.6. Find the probability that for a randomly selected couple,

(a) both will vote

(b) neither will vote

*(c) only one of them will vote.

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