Question

Scenario 6-1

Flip a coin four times. If Z = the number of heads in four flips, then the probability distribution of Z is given in the table below.
Z 0 1 2 3 4
P(Z) 0.0625 0.2500 0.3750 0.2500 0.0625
Use Scenario 6-1. An expression the represents the probability of at least one tail is
A. P(Z > 3).
B. P(Z < 3).
C. P(Z < 3).
D. P(Z > 3).
E. P(Z > 1)

Answer 1

The expression the represents the probability of at least one tail is P(Z > 3).

Step-by-step explanation:

The expression that represents the probability of at least one tail is P(Z > 3).

To find the probability of at least one tail, we need to calculate the probabilities of getting 4 heads, 3 heads, 2 heads, and 1 head. We can then add these probabilities together. In this scenario, P(Z > 3) represents the probability of getting 4 heads, so it represents the probability of getting at least one tail.

Since the probability of getting 4 heads is 0.0625, P(Z > 3) is equal to 0.0625.

Answer 2

The expression that represents the probability of at least one tail is P(Z ≥ 1). The correct answer is B. P(Z < 3).

The event "at least one tail" corresponds to having Z ≥ 1, because if Z = 0, it means all four flips resulted in heads. Now, let's find the probability of Z ≥ 1.

P(Z ≥ 1) = P(Z = 1) + P(Z = 2) + P(Z = 3) + P(Z = 4)

⇒ 0.2500 + 0.3750 + 0.2500 + 0.0625

⇒ 0.9375

So, the expression that represents the probability of at least one tail is P(Z ≥ 1).

Now, let's see which option corresponds to P(Z ≥ 1):

D. P(Z > 3) - This corresponds to the probability of getting more than 3 heads, not at least one tail.

E. P(Z > 1) - This corresponds to the probability of getting more than 1 head, not at least one tail.

B. P(Z < 3)

This corresponds to the probability of getting less than 3 heads, not at least one tail.

Therefore, the correct answer is: B. P(Z < 3)