Final answer:
The probability of drilling four dry wells before finding oil at the fifth attempt using the geometric distribution is 8.192%. The probability of asking fewer than four students before finding one who expects to work full-time in college is about 55.2%.
Step-by-step explanation:
To answer question 3 about the probability of drilling four dry wells before finding oil at the fifth one, we need to use the geometric distribution. The probability of finding oil on any given try is 0.20, and thus the probability of not finding oil is 1 - 0.20 = 0.80. To find the probability of the first occurrence of finding oil on the fifth drill, we calculate:
(0.80)4 × (0.20) = 0.4096 × 0.20 = 0.08192
Therefore, the probability is 0.08192, or about 8.192%.
For question 4, concerning the probability that you will ask fewer than 4 students before finding someone who expects to work full-time in college, we also apply the concept of geometric distribution. The probability can be calculated by 1 minus the probability of not finding such a student after three tries. That is:
1 - (0.766)3 = 1 - 0.448 = 0.552
The probability in this case is 0.552, or about 55.2%.