Question

from a srandard deck of 52 cards, what is the probability of drawing two five cards with replacement?

Answer 1

Event A = drawing a card with a "5" on the label.

There are 4 ways that event A could occur: drawing a '5' of hearts, 5 of spades, 5 of diamonds, or five of clubs.

This is out of 52 cards total

For one card,
P(A) = 4/52 = 1/13

For two cards,
P(A and A) = P(A)*P(A)
P(A and A) = (1/13)*(1/13)
P(A and A) = 1/169
We're able to multiply like this because the events are independent (replacement occurs).

The answer as a fraction is 1/169
The answer in decimal form is approximately 0.005917
The answer as a percent is approximately 0.5917%

Answer 2

There are 4 5's in a deck of 52 cards so
P(5) = 4/52
Since the card is being replaced it will be the same probability the second time.
P(5) = 4/52
P(5)= 4/52 * P(5)=4/52 = 16/2704 = 1/169