Final answer:
The probability that the first success occurs on the fourth trial, given a success probability of 0.30, is approximately 0.1029.
Step-by-step explanation:
The question asks to find the probability of the first success on the fourth trial, P(4), when the probability of success, p, is 0.30, assuming the geometric distribution applies. The probability of failure, q, is 1 - p, which is 0.70. The formula for the geometric probability of the first success on the x-th trial is given by P(x) = q^(x-1) * p. So for the fourth trial, P(4) will be calculated as follows:
- First, calculate q, the probability of failure: q = 1 - p = 1 - 0.30 = 0.70.
- Then, apply the formula: P(4) = q^(4-1) * p = 0.70^3 * 0.30.
- Compute: P(4) = 0.70^3 * 0.30 = 0.343 * 0.30 ≈ 0.1029.
The probability that the first success occurs on the fourth trial is approximately 0.1029.