Question

1. according to one study, 61% of the population swallow at least one spider per year in their sleep. based on this study, what is the probability that exactly 7 of 10 randomly selected people have swallowed at least one spider in their sleep in the last year?

a. 70%
c. 1%
b. 22%
d. 34%

Explanation:

Step1: Identify the distribution

This is a binomial probability problem. The binomial probability formula is \( P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k} \), where \( n = 10 \) (number of trials), \( k = 7 \) (number of successes), \( p = 0.61 \) (probability of success).

Step2: Calculate the combination

First, calculate the combination \( C(10,7)=\frac{10!}{7!(10 - 7)!}=\frac{10!}{7!3!}=\frac{10\times9\times8}{3\times2\times1}=120 \).

Step3: Calculate the probability

Then, \( p^{k}=(0.61)^{7}\approx0.0315 \), \( (1 - p)^{n - k}=(0.39)^{3}\approx0.0593 \).
Multiply them together: \( P(X = 7)=120\times0.0315\times0.0593\approx120\times0.001868\approx0.2242 \), which is approximately \( 22\% \).

Answer:

B. 22%