Question

Find the probability of selecting two number cards when two cards are

drawn (without replacement) from a standard deck of cards.

a) 105/221
b)105/676
c)314/221
d)315/676
Plz explain how you get your answer, Thank You!

Answer 1

We know that there are 36 number cards and 16 face cards in standard deck of 52 cards. Now choose two cards without replacement from 52 cards.

The number of ways of choosing any 2 cards without replacement from 52 cards is

C(2,52)=\frac{52!}{50!2!} .

The number of ways of choosing 2 number cards without replacement from 36 cards is

C(2,36)=\frac{36!}{34!2!} .

The required probability is

\frac{\frac{36!}{34!2!}}{\frac{52!}{50!2!} } =\frac{35*36}{51*52} =\frac{105}{221}

Correct choice is (A)

Answer 2

We know that there are 36 number cards and 16 face cards in standard deck of 52 cards. Now choose two cards without replacement from 52 cards.

The number of ways of choosing any 2 cards without replacement from 52 cards is

`C(2,52)=(52!)/(50!2!)`.

The number of ways of choosing 2 number cards without replacement from 36 cards is

`C(2,36)=(36!)/(34!2!)`.

The required probability is

`((36!)/(34!2!))/((52!)/(50!2!) ) =(35*36)/(51*52) =(105)/(221)`

Correct choice is (A).