Two cards are drawn at random from a pack of 52 cards. what is the probability that either both are

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Two cards can be drawn from 52 cards in 52C2 ways.∴ n(S) = `""^52"C"_2`Also, the pack of 52 cards consists of 26 red and 26 black cards.Let A be the event that both cards are black.

∴ 2 black cards can be drawn in 26C2 ways.


∴ n(A) = 26C2

∴ P(A) = `("n"("A"))/("n"("S"))=(""^26"C"_2)/(""^52"C"_2)=(26xx25)/(52xx51)=25/102`

Let B be the event that both cards are queens. There are 4 queens in a pack of 52 cards
∴ 2 queen cards can be drawn in 4C2 ways.

∴ n(B) = `""^4"C"_2`

∴ P(B) = `("n"("B"))/("n"("S")) =(""^4"C"_2)/(""^52"C"_2)= (4xx3)/(52xx51) = 1/221`There are two black queen cards.

∴ n(A ∩ B) = `""^2"C"_2` = 1

∴ P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S")) = 1/(""^52"C"_2)=(1xx2xx1)/(52xx51)`

= `1/1326`∴ Required probability = P(A ∪ B)

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= `25/102 + 1/221 - 1/1326`

= `325/1326 + 6/1236 - 1/1326`

= `330/1326`

= `55/221`

Q:

Find the range of the data 2, 1, 2, 3, 5, 4, 7, 3, 5, 2, 4.

Answer & Explanation Answer: D) 6

Explanation:


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