A box contains 20 cards marked with the numbers 1 to 20. One card is drawn from this box. What is the probability that number on the card is



5. A box contains 20 cards marked with the numbers 1 to 20. One card is drawn from this box. What is the probability that number on the card is

(i) a prime number

(ii) perfect square

(iii) multiple of 5

Sol. The sample space for box containing 20 cards

∴  S = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

∴  n (S) = 20

(i) Let A be the event that number on the card is prime

A = { 2, 3, 5, 7, 11, 13, 17, 19 }

n (A) = 8

P (A) = n (A)/n (S)

∴  P (A) = 8/20

∴  P (A) = 2/5



(ii) Let B be the event that number on the card is a perfect square

B = { 1, 4, 9, 16 }

n (B) = 4

P (B) = n (B)/n (S)

∴  P (B) = 4/20

∴  P (B) = 1/5



(iii)Let C be the event that number on the card is multiple of 5

C = { 5, 10 15, 20 }

n (C) = 4

P (C) = n (C)/n (S)

∴  P (C) = 4/20

∴  P (C) = 1/5

No comments:

Post a Comment