Questions: The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. Is Avery interpreting the probability correctly? (A) Yes, because 2 out of 5 is equal to 40%. (B) Yes, because participants in the survey are selected at random. (C) No, because there could be voluntary response bias. (D) No, because only 40% of all people will visit the site.

Solution Steps

The problem involves determining whether Avery's interpretation of the probability is correct. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. The probability of a visitor being asked to participate is 0.40.

Avery's claim implies that exactly 2 out of the next 5 visitors will be asked to participate in the survey. This is a binomial probability problem where the number of trials \( n = 5 \), the probability of success (being asked to participate) \( p = 0.40 \), and the number of successes \( k = 2 \).

The probability of exactly 2 out of 5 visitors being asked to participate can be calculated using the binomial probability formula:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

Substituting the values:

\[ P(X = 2) = \binom{5}{2} (0.40)^2 (0.60)^3 \]

Calculating each component:

\[ \binom{5}{2} = 10 \] \[ (0.40)^2 = 0.16 \] \[ (0.60)^3 = 0.216 \]

Thus, the probability is:

\[ P(X = 2) = 10 \times 0.16 \times 0.216 = 0.3456 \]

• Option A: Incorrect. While 2 out of 5 is 40%, the probability of exactly 2 out of 5 being asked is not 100%.
• Option B: Incorrect. Random selection does not guarantee exactly 2 out of 5.
• Option C: Incorrect. Voluntary response bias is not relevant to the probability calculation.
• Option D: Incorrect. The statement about 40% of all people visiting the site is irrelevant to the probability of selection.

Final Answer