Respuesta :
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
The probability of drinking alcohol and being over 21 years old is [tex]\boxed{0.24{\text{ or 24\% }}}[/tex]. 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.
[tex]30\%[/tex] 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,
[tex]P\left( X \right) = 0.3[/tex]
The probability of drinking alcohol is 0.8.
The probability of drinking alcohol and being over 21 years can be obtained as follows,
[tex]\begin{aligned}{\text{Probability}}&= P\left( X \right) \times P\left( {Y/X} \right)\\&= 0.3 \times 0.8\\&= 0.24\\\end{aligned}[/tex]
The probability of drinking alcohol and being over 21 years old is [tex]\boxed{0.24{\text{ or 24\% }}}[/tex]. Option (c) is correct.
Learn more:
- Learn more about normal distribution https://brainly.com/question/12698949
- Learn more about standard normal distribution https://brainly.com/question/13006989
- 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.
