Question

Given that the first 5 flips are heads, find the conditional probability the first tail is obtained on the 9th coin flip.

a) 1/2
b) 1/4
c) 1/8
d) 1/16

Answer 1

The conditional probability of obtaining the first tail on the 9th coin flip, given that the first 5 flips are heads, is 1/32.

Step-by-step explanation:

To find the conditional probability that the first tail is obtained on the 9th coin flip, given that the first 5 flips are heads, we need to consider the sample space of possible outcomes. When the first 5 flips are heads, there are 2 outcomes for the 6th flip (H or T). Similarly, there are 2 outcomes for the 7th and 8th flips. Finally, there is only 1 outcome for the 9th flip (T). Therefore, the sample space has a total of 2*2*2*2*2*1 = 32 outcomes. Out of these 32 outcomes, only 1 outcome satisfies the condition that the first tail is obtained on the 9th flip. Therefore, the probability is 1/32.