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Question
A single card is drawn from a pack of 52 cards. What is the probability that the card will be 6 or smaller
Solution
S be the sample space one card is drawn from a pack of 52 cards.
∴ n(S) = 52C1
n(S) = 52
The card will be 6 or smaller:
Let A be the event of getting a number 6.
∴ n(A) = 4C1 = 4
Let B be the event of getting numbers less than 6.
n(B) = 16C1 = 16
P (the card will be 6 or less than 6)
= P(A or B)
= P(A ∪ B)
= P(A) + P(B)
(since A and B are mutually exclusive events A ∩ B = Φ)
= `("n"("A"))/("n"("S")) + ("n"("B"))/("n"("S"))`
= `4/52 + 16/52`
= `(4 + 16)/52`
= `20/52`
= `5/13`
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