Question

(1 point) what is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails?

a. 0.0625
b. 0.125
c. 0.25
d. 0.5

Answer 1

Option (b), The conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, is 0.125.

Step-by-step explanation:

The conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, can be calculated using the formula for conditional probability:

P(4 heads | first flip = tails) = P(4 heads and first flip = tails) / P(first flip = tails)

Since there are 5 coin flips and each flip is independent, the probability of getting exactly four heads and the first flip being tails is given by:

P(4 heads and first flip = tails) = P(4 heads) * P(first flip = tails) = (0.5)^4 * 0.5 = 0.0625

The probability of the first flip being tails is simply 0.5, since the coin is fair. Therefore:

P(4 heads | first flip = tails) = 0.0625 / 0.5 = 0.125

Therefore, the correct answer is option b. 0.125.