Final answer:
To calculate the probabilities, use the binomial probability formula and plug in the given values. For part (a), calculate the probability of exactly four successful surgeries. For part (b), calculate the probability of less than four successful surgeries. For part (c), calculate the probability of at least two successful surgeries.
Step-by-step explanation:
To find the probability for each part of the question:
(a) The probability of exactly four surgeries being successful can be calculated using the binomial probability formula. The formula is P(x) = C(n, x) * p^x * q^(n-x), where n is the total number of surgeries, x is the number of successful surgeries, p is the success rate, and q is the failure rate. Plugging in the values, we have P(4) = C(5, 4) * 0.94^4 * 0.06^1. Calculate this expression to find the probability.
(b) The probability of less than four surgeries being successful is the sum of the probabilities of exactly zero, one, two, and three surgeries being successful. Calculate each of these probabilities using the binomial probability formula and add them up to find the total probability.
(c) The probability of at least two surgeries being successful is the sum of the probabilities of exactly two, three, four, and five surgeries being successful. Calculate each of these probabilities using the binomial probability formula and add them up to find the total probability.