A recent survey shows that the probability of a college student drinking alcohol is 0.6. further, given that the student is over

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A recent survey shows that the probability of a college student drinking alcohol is 0.6. further, given that the student is over

21 years old, the probability of drinking alcohol is 0.8. it is also known that 30% of the college students are over 21 years old. what is the probability of drinking alcohol and being over 21 years old? 0.66 0.36 0.24 0.42

Mathematics

2 answers:

AnnZ [9K] · Answer 1 · 2026-03-27T05:14:28+03:00

Answer:

0.24

Explanatory steps:

These events can occur simultaneously, indicating they are not mutually exclusive.

For events A and B where mutual exclusivity does not apply,

P(A and B) = P(A) * P(B|A)

Let A represent the event of being "over 21 years old" and B represent the event of "consuming alcohol."

The likelihood of a student being over 21 years is 0.3, reflecting that 30% of the students are in that age range.

The probability that a student consumes alcohol given they are over 21 stands at 0.8.

This results in

P(A and B) = 0.3(0.8) = 0.24

AnnZ [9K] · Answer 2 · 2026-03-27T05:15:27+03:00

The chance of consuming alcohol while being older than 21 years is $\boxed{0.24{\text{ or 24\% }}}$ . The correct answer is option (c).

Additional Details:

Given:

The chance of a college student drinking alcohol stands at 0.6.

The chance of consuming alcohol is 0.8.

of the college student population is over 21 years of age.

Explanation:

Let X represent the event of being over 21 years old.

Let Y denote the event of drinking alcohol.

The probability of event X can be calculated as follows,

$P\left( X \right) = 0.3$

The chance of alcohol consumption equals 0.8.

To find the joint probability of drinking alcohol and being over 21, we can use the following method,

$\begin{aligned}{\text{Probability}}&= P\left( X \right) \times P\left( {Y/X} \right)\\&= 0.3 \times 0.8\\&= 0.24\\\end{aligned}$

The likelihood of both drinking alcohol and being older than 21 years is $\boxed{0.24{\text{ or 24\% }}}$ . Option (c) is indeed correct.

Learn more:

Discover more about normal distribution
Discover more about standard normal distribution
Learn more about confidence interval of meanhttps://[[TAG_74]][[TAG_75]]

Answer details:

Grade: College

Subject: Statistics

Chapter: Conditional Probability

Keywords: Probability, students, alcohol, survey, recent, college, drinking alcohol, college student, 30% of college student, 21 years old, being over, 0.6, 0.8.