Question

The probability htat a randomly selected patient who visits the emergency room (ER) will die within 1 year of the visit is 0.05.

a. What is the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year? Interpret this result.

A) 0.05
B) 0.59874
C) 0.37735
D) 0.12346

Answer 1

The probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year is 0.37735.

Step-by-step explanation:

To find the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year, we can use the binomial probability formula.

The formula is:

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

where:

- P(X = k) is the probability of getting exactly k successes,

- n is the number of trials,

- k is the number of successes,

- p is the probability of success.

In this case, n = 10, k = 1, and p = 0.05.

Plugging in these values, we get:

P(X = 1) = C(10, 1) * (0.05)^1 * (1-0.05)^(10-1)

Calculating this, we find:

P(X = 1) = 0.37735

Therefore, the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year is 0.37735.

This means that out of every 10 visitors to the ER, we can expect, on average, 1 person to die within 1 year.