Question

In a sample of 800 adults, 242 said that they liked sugar cereals. Three adults are selected at random without replacement. Find the probability that all three like sugar cereals.

Answer 1

Answer:

$P(A) = 0.0274$

Step-by-step explanation:

Given

$n = 800$ --- Population

$A = 242$ --- those that liked sugar cereals

Required

Probability that three selected like sugar cereals

The probability that the first adult selected likes sugar cereals is:

$P(A_1) = \frac{242}{800}$

The probability that the second adult selected likes sugar cereals is:

$P(A_2) = \frac{242-1}{800-1} = \frac{241}{799}$

We subtracted 1 because it is a probability without replacement

Similarly:

$P(A_3) = \frac{241-1}{799-1} = \frac{240}{798}$

The required probability is calculated as follows:

$P(A) = P(A_1) * P(A_2) * P(A_3)$

$P(A) = \frac{242}{800} * \frac{241}{799} * \frac{240}{798}$

$P(A) = \frac{242*241*240}{800*799*798}$

$P(A) = \frac{13997280}{510081600}$

$P(A) = 0.0274$