Question

2. Ron’s Joke Store offers a coin that is supposed to be weighted toward heads. Caitlin tries out one of these coins.

She flips the coin three times and gets a head on all three flips.
a. If the coin was fair, what would the probability be that Caitlin would get heads on all three flips? (Round your
answer to the nearest thousandth.)
b. Should Caitlin’s result of heads on all three flips lead her to conclude that the coin is weighted toward heads?
Explain.

Answer 1

a) P = 0.125

b) It is not necessarily true

Explanation:

a. If the coin was fair, the probability of obtaining head would be 0.5, and each launch of the coin would be an independent event.

Remember that if two events A and B are independent, then:

P(A∩B) = P(A)P(B)

Therefore, the probability that Caitlin would get heads on all three flips is:

P(A∩A∩A) = P(A)P(A)P(A) = 0.5*0.5*0.5 = 0.125

b) It is not necessarily true, because there exist a probability associated to this event and it means that this situation can occur although the coin was fair.