Question

Help Me PLEASE!!!

A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a diamond or an ace?

Answer 1

P = 0.5207

Explanation:

First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.

Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).

So, the probability that just the first card is a diamond or an ace is calculated as:

`P_1=(16)/(52)*(36)/(52)=0.2130`

At the same way, the probability that just the second card is a diamond or an ace is:

`P_2=(36)/(52)*(16)/(52)=0.2130`

Finally, the probability that both cards are diamonds or aces is:

`P_3=(16)/(52)*(16)/(52)=0.0947`

Therefore, the probability that at least one of the cards is a diamond or an ace is:

`P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207`