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

answer:

B. 22%

thank you.

To find the probability that exactly 7 out of 10 randomly selected people have swallowed at least one spider in their sleep, we can use the binomial probability formula.

The binomial probability formula is given by P(X=k) = nCk * p^k * q^(n-k), where:
- P(X=k) is the probability of exactly k successes (swallowing a spider)
- nCk is the number of ways to choose k items from a set of n items (combination)
- p is the probability of success (swallowing a spider)
- q is the probability of failure (not swallowing a spider)
- k is the number of successes (people who have swallowed a spider)
- n is the total number of trials (number of people selected)

In this case, the probability of success (p) is 61% or 0.61, and the probability of failure (q) is the complement of p, which is 1 - 0.61 = 0.39. The total number of trials (n) is 10, and we want to find the probability of exactly 7 successes (k=7).

Inserting these values into the formula, we have:
P(X=7) = 10C7 * 0.61^7 * 0.39^(10-7)

Calculating the values, we get:
10C7 = (10!)/(7!(10-7)!) = 120
0.61^7 = 0.0248
0.39^(10-7) = 0.0399

Now, substitute these values into the formula:
P(X=7) = 120 * 0.0248 * 0.0399

Calculating this, we find:
P(X=7) ≈ 0.118

Therefore, the probability that exactly 7 out of 10 randomly selected people have swallowed at least one spider in their sleep is approximately 0.118 or 11.8%.

Since none of the given answer choices match the correct answer, there might have been an error in the question or answer options you provided. Please double-check the information provided.

To calculate the probability, we need to use the binomial probability formula. Given that the probability of a randomly selected person swallowing at least one spider in their sleep is 61%, we can use this as the probability of success (p).

We have 10 randomly selected people and we want to find the probability that exactly 7 of them have swallowed at least one spider in the last year.

Using the formula for binomial probability, we can calculate it as follows:

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

Where:
P(X = k) is the probability of exactly k successes
n is the number of trials (in this case, 10 randomly selected people)
k is the number of successes we want (in this case, 7)
p is the probability of success (in this case, 61% or 0.61)
(1 - p) is the probability of failure (in this case, 39% or 0.39)

Plugging in the values:

P(X = 7) = (10C7) * 0.61^7 * 0.39^(10 - 7)
P(X = 7) = 120 * (0.61)^7 * (0.39)^3
P(X = 7) ≈ 0.2251

Therefore, the probability that exactly 7 of the 10 randomly selected people have swallowed at least one spider in their sleep in the last year is approximately 22% (0.2251).

So, the correct answer is B. 22%.