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in Statistics and Probability by (47.8k points)
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At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that

(i) the first player wins a prize

(ii) the second player wins a prize if the first has won?

1 Answer

+1 vote
by (47.4k points)
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Best answer

Sample space = {1, 2, 3,… ,1000}

n(S) = 1000

(i) Let A be the event of setting square number greater than 500

A = {529, 576, 625, 676, 729, 784, 841, 900, 961}

n(A) = 9

P(A) = \(\frac{n(A)}{n(S)}=\frac{9}{1000}\)

The probability that the first player wins prize = \(\frac{9}{1000}\)

(ii) If the first player wins, the number is excluded for the second player.

n(A) = 8 and n(S) = 999

P(A) = \(\frac{n(A)}{n(S)}=\frac{8}{999}\)

Probability the second player wins a prize = \(\frac{8}{999}\)

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