Question

A card from a 52 card deck is lost. We then draw 2 cards from the 51 remaining cards. What is the probability they are both diamonds?

Answer 1

Answer:

$\frac{1}{17}$

Explanation:

Let D be the event that the lost card is a diamond

and D' be the event that the lost card is a non diamond

Therefore,

P(D) = $\frac{13}{52}$ = 0.25

P(D') = $\frac{39}{52}$ = 0.75

Now,

Event that the cards picked up are both diamonds = A

Thus,

P( A | D) = $\frac{12}{51 }\times\frac{11}{50}$               [ As One Diamond Card is lost ]

And,

P(A | D') = $\frac{13}{51}\times\frac{12}{50}$                [ As One Non-Diamond card is lost ]

Therefore,

P(A) = P(D) × P(A | D) + P(D') × P( A | D')  

= 0.25 × $\frac{12}{51 }\times\frac{11}{50}$  + 0.75 ×  $\frac{13}{51}\times\frac{12}{50}$

= $\frac{1}{17}$