Question

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

Answer 1

Answer:

0.24

Step-by-step explanation:

These events are not mutually exclusive; this means they can happen at the same time.

For two events A and B that are not mutually exclusive,

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

Let A be the event "over 21 years old" and B be the event "drinks alcohol".  

The probability that a student is over 21 years old is 0.3; this is because 30% of the students are over 21 years old.

The probability that a student drinks alcohol given they are over 21 is 0.8.

This gives us

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

Answer 2

The probability of drinking alcohol and being over 21 years old is $\boxed{0.24{\text{ or 24\% }}}$. Option (c) is correct.

Further Explanation:

Given:

The probability of a college student drinking alcohol is 0.6.

The probability of drinking alcohol is 0.8.

$30\%$ of the college students are over 21 years old.

Explanation:

Consider X be the event that a student is over 21 years old.

Consider Y be the event that a student drinks alcohol.

The probability of event X can be expressed as follows,

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

The probability of drinking alcohol is 0.8.

The probability of drinking alcohol and being over 21 years can be obtained  as follows,

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

The probability of drinking alcohol and being over 21 years old is $\boxed{0.24{\text{ or 24\% }}}$. Option (c) is correct.

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949
2. Learn more about standard normal distribution brainly.com/question/13006989
3. Learn more about confidence interval of meanhttps://brainly.com/question/12986589

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.