Final answer:
The probability distribution of X can be modeled with a binomial distribution. The probability of drilling four dry wells before finding oil on the fifth one is approximately 8.19%.
Step-by-step explanation:
a) Probability Distribution of X:
The probability distribution of X can be modeled using a binomial distribution, since each drilling operation has two possible outcomes: finding oil (success) or not finding oil (failure).
Given that the probability of finding oil is 0.20, the probability distribution of X can be represented by:
P(X = x) = (0.20)^x * (1-0.20)^(5-x) * C(n, x), where x = 0, 1, 2, 3, 4, 5 and C(n, x) represents the combination formula.
b) Probability of 4 Dry Wells Before Finding Oil on the Fifth:
To find the probability of drilling four dry wells before finding oil on the fifth one, we need to calculate the probability of exactly four failures (dry wells) followed by one success (finding oil).
P(X = 4) = (0.80)^4 * 0.20 = 0.08192, or approximately 8.19%.