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Find the probabilities of the events

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.

PROBABILITY TOPICS

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d. Are F and G mutually exclusive?

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

Look at the sample space in Example 3.6.

a. Zero (0) or one (1) tails occur when the outcomes HH, TH, HT show up. P(F) =

b. Two faces are the same if HH or TT show up. P(G) =

c. A head on the first flip followed by a head or tail on the second flip occurs when HH or HT show up. P(H) =

d. F and G share HH so P(F AND G) is not equal to zero (0). F and G are not mutually exclusive.

e. Getting all tails occurs when tails shows up on both coins (TT). H’s outcomes are HH and HT.

J and H have nothing in common so P(J AND H) = 0. J and H are mutually exclusive.

3.7 A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:

a. Let F = the event of getting the white ball twice.

b. Let G = the event of getting two balls of different colors.

c. Let H = the event of getting white on the first pick.

d. Are F and G mutually exclusive?

e. Are G and H mutually exclusive?