Question

The survival rate during a risky operation for patients with no other hope of survival is 82%. What is the probability that exactly four of the next five patients would survive this operation?

A) 0.5904
B) 0.082
C) 0.18048
D) 0.16384

Answer 1

The probability that exactly four of the next five patients would survive this operation is 0.5904.

Step-by-step explanation:

To find the probability that exactly four of the next five patients would survive the operation, we need to use the binomial probability formula. The formula is:

P(k) = C(n, k) * p^k * (1-p)^(n-k)

where:

• P(k) is the probability of exactly k successes
• C(n, k) is the number of combinations of n items taken k at a time
• p is the probability of success in one trial
• n is the total number of trials

In this case:

• k = 4
• p = 0.82 (survival rate)
• n = 5 (number of patients)

Plugging in the values:

P(4) = C(5, 4) * 0.82^4 * (1-0.82)^(5-4)

= 5 * 0.82^4 * 0.18

= 0.5904

Therefore, the probability that exactly four of the next five patients would survive this operation is 0.5904.