Five hundred consumers are surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
$Unknown environment 'tabular'$
One consumer from the survey is selected at random. Leave all answers in a reduced fraction.
a. What is the probability that the consumer is $18 - 24$ years of age, given that he/she dislikes Crunchicles?
b. What is the probability that the selected consumer dislikes Crunchicles?
c. What is the probability that the selected consumer is $35 - 55$ years old or likes Crunchicles?
d. If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?

Answer

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Answer

$\frac{40}{121}$

Steps

Step 1 ：Find the probabilities P(A and B) and P(B) from the given table:

Step 2 ： $P (A and B) = \frac{40}{500} = 0.08$

Step 3 ： $P (B) = \frac{121}{500} = 0.242$

Step 4 ：Calculate the conditional probability P(A|B) using the formula P(A|B) = P(A and B) / P(B):

Step 5 ： $P (A | B) = \frac{0.08}{0.242} = \frac{40}{121}$

Step 6 ： $\frac{40}{121}$