Question

two cards are drawn from a pack of 52 cards. what is the probability that either both are ace or black?​

Answer 1

Answer:

We have n(s) =52C2 52 = 52*51/2*1= 1326.  

Let A = event of getting both black cards  

    B = event of getting both queens  

A∩B = event of getting queen of black cards  

n(A) = 52*512*1 = 26C2 = 325, n(B)= 26*252*1= 4*3/2*1= 6  and  n(A∩B) = 4C2 = 1  

P(A) = n(A)/n(S) = 325/1326;

P(B) = n(B)/n(S) = 6/1326 and  

P(A∩B) = n(A∩B)/n(S) = 1/1326  

P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 = 55/221

Step-by-step explanation:

Answer 2

Answer:

Assuming, you meant, cards are drawn without replacement:

P(both black) = 26/52 x 25/51 = 650/2652

P(both queens) = 4/52 x 3/51 = 12/2652

P(both black & queens) = 2/52 x 1/51 = 2/2652

We use the basic addition rule,

P(both black or both queens) = P(both black) + P(both queens) - P(both black as well as queens)

= 650/2652 + 12/2652 - 2/2652

= 660/2652 = 0.24886

Hope this helps