1. An arcade booth at a county fair has a person pick a coin from two possible c

Question

1. An arcade booth at a county fair has a person pick a coin from two possible coins available and then toss it. If the coin chosen lands on heads, the person gets a prize. One coin is a fair coin and one coin is a biased coin (unfair) with only a 36% chance of getting a head. Assuming equally likely probability of picking either coin, what is the probability that the fair coin is the one chosen, given that the chosen coin lands on heads?

a) 0.4098

b) 0.4300

c) 0.0137

d) 0.8600

e) 0.5814

f) None of the above.

2. King Mattress purchases Sleep-n-Air mattresses from three different distributors. The probability of getting a defective mattress from Distributor A, B, or C is 0.31, 0.52, and 0.15, respectively. Assume an equal probability of making a purchase from each distributor A, B, or C. If King Mattress sells a defective mattress, what is the probability that it came from Distributor A?

a) 0.0968

b) 0.1531

c) 0.0577

d) 0.5306

e) 0.3163

f) None of the above.

Explanation / Answer

1)

P( Fair/Head) = P(Head/Fair)*P(Fair) / [ P(Head/Unfair)*P(Unfair) + P(Head/Fair)*P(Fair)] = 0.50/[0.36+0.50]=50/86= 0.5813

2)

Required probability = 0.31/ [0.31+0.52+0.15] = 0.3163

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