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?

See explanation

Step-by-step explanation:

Given

Represent the balls with the first letters

Solving (a): P(F) --- White balls twice

The event of F is:

So:

Solving (b): P(G) --- two different colors

The event of G is:

So:

Solving (c): P(H) --- White picked first

The event of H is:

So:

Solving (d): F and G, mutually exclusive?

We have:

Check for common elements

Hence, F and G are mutually exclusive

Solving (e): G and G, mutually exclusive?

We have:

Check for common elements

Hence, F and G are not mutually exclusive

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