Question

A fair coin is flipped three times. Events A and B are defined as: A: there are at least two consecutive heads somewhere in the sequence B: at least one flip comes up tails What is p(A|B) ?

a. 1/4
b. 2/7
c. 3/8
d. 1/2

Answer 1

The probability of event A given that event B has occurred is undefined because events A and B cannot occur together.

Step-by-step explanation:

Let's consider the events A and B defined in the question:

A: there are at least two consecutive heads somewhere in the sequence

B: at least one flip comes up tails

To find P(A|B), which is the probability of event A given that event B has occurred, we can use the formula:

P(A|B) = P(A ∩ B) / P(B)

To find P(A ∩ B), we need to find the probability of both events A and B occurring together.

In this case, it is not possible for event A and event B to occur together because event A requires consecutive heads, while event B requires at least one flip to be tails.

Therefore, P(A ∩ B) = 0, and since we cannot divide by 0, the value of P(A|B) is undefined. So, there is no valid answer among the given options.