Question

a board game uses the deck of 20 cards shown to the right. two cards are selected at random from this deck. calculate the probability that both cards selected have a 5, both with and without replacement. two cards are to be selected with replacement. determine the probability that both cards selected have a 5. 1/25 (type an integer or a simplified fraction.) two cards are to be selected without replacement. determine the probability that both cards selected have a 5. (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the number of cards with a 5

There are 4 cards with a 5 in the deck of 20 cards.

Step2: Probability without replacement

The probability of drawing a 5 - card first is $\frac{4}{20}$.
After drawing one 5 - card (without replacement), there are 3 five - cards left and 19 cards in total. So the probability of drawing a 5 - card second is $\frac{3}{19}$.
The probability that both cards are 5 - cards (without replacement) is the product of these two probabilities: $P=\frac{4}{20}\times\frac{3}{19}$.

Answer:

$\frac{3}{95}$