Question

Example 2
Two cards are drawn from a pack of cards. Find the probability that they will be both red or both pictures.
*WITH STEP BY STEP AND PROPER EXPLANATION*
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Answer 1

Step-by-step explanation:

Let S : Drawing 2 cards out of 52 card  A : Drawing 2 red cards  B : Drawing 2 kings  A ∪ B : Drawing 2 red cards or 2 kings  ∴ n(S) = 52C2  n(A) = 26C2          (∵ There are 26 red cards)  n(B) = 4C2          (∵ There are 4 kings)  But there are 2 red kings, so  A ∩ B : Drawing 2 red kings  ⇒ n(A ∩ B) = 2C2.  ∴ Required probability = P(A∪B) = P(A) + P(B) – P(A ∩ B) =  n ( A ) n ( S ) n(A)n(S) +  n ( B ) n ( S ) n(B)n(S) -  n ( A ∩ B ) n ( S ) n(A∩B)n(S) =  26 C 2 52 C 2 26C252C2 +  4 C 2 52 C 2 4C252C2 -  2 C 2 52 C 2 2C252C2 =  26 × 25 52 × 51 26×2552×51 +  4 × 3 52 × 51 4×352×51 -  2 52 × 51 252×51 =  660 2652 6602652 =  55 221