A survey of 1,000 Canadian sports fans who indicated they were either hockey fan

Question

A survey of 1,000 Canadian sports fans who indicated they were either hockey fans or lacrosse fans or bot, had the following result. 800 indicated that they were hockey fans 600 indicated that they were lacrosse fans Based on the sample, find the probability that a Canadian sports Van is not a hockey fan given that he/she is a lacrosse fan. A) 1/5 B) 1/4 C) 1/3 D) 1/2 E) 1 (c) A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and without replacement. Calculate the probability that the number of boys exceeds the number of girls selected. A) 512/3375 B) 28/65 C) 8/15 D) 1856/3375 E) 36/65

Explanation / Answer

(b)

Let H shows the event that person is a hockey fan and L shows the event that person has lacrosse fan. So we have

P(H or L) = 1000 /1000 =1

P(H) = 800 /1000 =0.8

P(L) = 600 /1000 =0.6

So by the addition rule we have

P(H and L) = P(H) + P(L) - P(H or L) = 0.8+0.6 -1 = 0.4

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P(not H and L) = P(L) - P(H and L) = 0.6 - 0.4 = 0.2

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The required conditional probability is

P(not H | L) = P(not H and L) / P(L) = 0.2 / 0.6 = 1/3

Hence, option c is correct.

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