Final answer:
The probability of a single, successful phase in the first six phases of meiosis is approximately 89.87%, while the probability of passing each one of the last two phases is approximately 90.45%, assuming independent and constant probabilities throughout.
Step-by-step explanation:
Probability of Passing Phases in Meiosis
The process of meiosis includes a series of eight different phases, and only a certain percentage of processes pass through each of these phases. According to the given data, 55% of the processes pass the first six phases, and out of these, 45% pass all eight. To find the probability of a successful pass of a single one of the first six phases, you must find the sixth root of 0.55, as the events are independent and constant. Similarly, for the last two phases, since we know that 45% pass all eight phases, you first divide 0.45 by 0.55 to find the conditional probability of passing the last two phases given that the first six were passed, and then find the square root of that value to get the probability of passing a single phase among the last two.
(a) If the probability of a successful pass of each one of the first six phases is constant, we can use the formula for independent events: P(A)^6 = 0.55, where P(A) is the probability we're looking for. Solving for P(A) would be equivalent to taking the sixth root of 0.55, which yields P(A) ≈ 0.8987, or approximately 89.87% for each phase.
(b) If the probability of a successful pass of each one of the last two phases is constant, we first find the conditional probability of passing these phases given that the first six were passed, by using the formula P(B|A) = P(B and A) / P(A). Thus, P(B|A) = 0.45 / 0.55. After finding this probability, which is P(B|A) ≈ 0.8182, we calculate the probability for a single one of these phases. This is done by taking the square root, giving us P(B) ≈ 0.9045, or approximately 90.45% for each phase.