4. When people apply to a certain club one of the requirements is that they must

Question

4. When people apply to a certain club one of the requirements is that they must take an IQ test. O f the 100 people applying during the month of May, 90% are able to join, and 10% are not. Of those people, those eligible to join score more than a certain level on the IQ test 91% of the time while people ineligible to join pass the IQ test 26% of the time. What is the probability that an applicant during May passes the IQ test? Round your answer to four decimal places. 5. Find the probability of obtaining exactly 3 heads in 4 tosses of a fair coin. 6. A batter gets a hit on the average of once every 7 times he is at bat. If this batter is at bat 10 times, what is the probability that exactly 9 at bats result in hits?

Explanation / Answer

4) Let P(J = Joining ) = 0.9, P(NJ = Not eligible to Join) = 0.1

Let P(P/J = Those who have passed given that they have Joined) = 0.91, and

P(P/NJ = Those who have passed, given that they were not eligible) = 0.26

To Find P(P = Passing)

P(P) = P(P/J) x P(J) + P(P/NJ) x P(NJ)

= (0.91x0.9) + (0.26x0.1)

= 0.819 + 0.026

P(P) = 0.845

5) Tossing 1 coin 4 times is the same as tossing 4 coins once. The total number of outcomes is 2n = 24 = 16

The Favourable outcomes are 4 {HHHT}, {HHTH}, {HTHH}, {THHH}

Therefore the required probability = 4/16 = 1/4 = 0.25

6) Binomial Probability = nCx * (p)x * (q)n-x, where n = number of trials and x is the number of successes.

and nCx = n! / [(n-x)!*x!]

P(Hit) = p = 1/7, q = 1 - 1/7 = 6/7, n = 10 and x = 9

P(X= 9) = 10C9 * (1/7)9 * (6/7)1 = 0.0000002

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