Question

1). Suppose we have two coins, coin A and coin B, and flip them each 10 times. Let E be the event that every time coin A comes up heads, so does coin B. Find P(E).

2). Suppose we have 10 people, 5 on team A and 5 on team B. After a competition, they are ranked from 1 to 10. Let X be the best ranking obtained by a member of team A (i.e. if a person from team A wins, then X = 1). Find P(X = i) for i = 1, . . . , 10.

Answer 1

1:

When we flip a coin possible outcomes are head and tail. The probability of getting a head in a single toss is

p = P(head) = 0.5

Since tosses are independent so we need to use multiplication rule. The probability that we get all 10 heads for coin A is

The probability that we get all 10 heads for coin B is

Since coins A and B are independent so the probability of event E is

Answer: 0.0000009537