Question

1a)

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 35% 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) 0.8500

b) 0.0141

c) 0.4250

d) 0.4167

e) 0.5882

f) None of the above.

1b)

There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 15 chocolate chip and 9 sugar cookies. The green jar contains 6 chocolate chip, 11 sugar and 10 peanut butter cookies. The pink jar contains 5 chocolate chip, 7 sugar and 14 peanut butter cookies. One of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will be chosen are ¹⁄₂ , ¹⁄₄ , and ¹⁄₄ , respectively. A cookie is then chosen at random from the chosen jar. What is the probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie?

a) 0.2692

b) 0.1887

c) 0.0897

d) 0.0673

e) 0.2560

f) None of the above.

Answer 1