Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# A box contains cards numbered 3, 5, 7, 9, … 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number. - Mathematics

Sum

A box contains cards numbered 3, 5, 7, 9, … 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.

#### Solution

Sample space = {3, 5, 7, 9, ... 35, 37}

n(S) = 18

Let A be the event of getting a multiple of 7

A = {7, 21, 35}

n(A) = 3

P(A) = ("n"("A"))/("n"("S")) = 3/18

Let B be the event of getting a prime number

B = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}

n(B) = 11

P(B) = ("n"("B"))/("n"("S")) = 11/18

A ∩ B = {7}

n(A ∩ B) = 1

P(A ∩ B) = ("n"("A" ∩ "B"))/("n"("S")) = 1/18

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

= 3/18 + 11/18 - 1/18

= (3 + 11 - 1)/18

= 13/18

Probability of getting a multiple of 7 or a prime number = 13/18

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