A box has three balls, one white and two 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 explaation

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

assuming you mean addition: addition and subtraction are reverse operations.

step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5