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StatisticsProbability

Define Mutually Exclusive Events: Two Fair-Coin Probabilities

Use the four outcomes of two fair coins to calculate five event probabilities and decide which pairs share an outcome.

Question

Flip two fair coins. Find the probabilities of the events.

a. Let F = the event of getting at most one tail (zero or one tail).

b. Let G = the event of getting two faces that are the same.

c. Let H = the event of getting a head on the first flip followed by a head or tail on the second flip.

d. Are F and G mutually exclusive?

e. Let J = the event of getting all tails. Are J and H mutually exclusive?

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Evidence boundary

This answer uses OpenStax Example 3.7 from the 2013 PDF, retaining all five parts. Probabilities use the textbook model of two independent fair coins, with the coins distinguished by order. No actual coin-toss observations are claimed.