Question

Two cards are drawn in succession from a standard​ 52-card deck. What is the probability that the first card is a heart and the second card is a diamond (Upper A )If the cards are drawn without​ replacement? (Upper B )If the cards are drawn with​ replacement?

Answer 1

Answer: The required probabilities are

(A) 0.0637

(B) 0.0625.

Step-by-step explanation: Given that two cards are drawn in succession from a standard​ 52-card deck.

We are to find the probability that the first card is a heart and the second card is a diamond

(A) if the cards are drawn without​ replacement.

(B) If the cards are drawn with​ replacement.

We know that in a deck of 52 cards, there are 13 hearts and 13 diamonds.

(A) If the cards are drawn without replacement, then in the second turn, we are left with 51 cards.

Therefore, the probability is given by

`p=(13)/(52)*(13)/(51)=(13)/(204)=0.0637.`

(B) If the cards are drawn with replacement, then in the second turn, we are again left with 52 cards.

Therefore, the probability is given by

`p=(13)/(52)*(13)/(52)=(1)/(16)=0.0625.`

Thus, the required probabilities are

(A) 0.0637

(B) 0.0625.