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At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. What is the probability that a randomly selected student studies for a test and gets a B or higher?

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brycelaw318

Answer:

The probability that a randomly selected student studies for a test and gets a B or higher is 33%.

Step-by-step explanation:

What we know:

There is a 55% chance a student will get a B or higher on the tests.

60% of students study for the tests.

P(A∩B) = P(A) * P(B)

P(A∩B) = 3/5 * 11/20

P(A∩B) = 33/100 = 0.33 = 33% chance to get a B when studying for a test.

MrRoyal

Probabilities are used to determine the chances of passing a test and getting a B grade

The probability that a selected student studies, and gets B or higher is 33%

Let the events be represented as follows:

  • A: The event that a student gets B or higher in a test if they study
  • B: The event that a student gets B or higher in a test if they do not study

So, we have:

[tex]\mathbf{P(A) = 55\%}[/tex]

[tex]\mathbf{P(B) = 20\%}[/tex]

60% of the students study.

So, the probability that a student studies, and gets B or higher is:

[tex]\mathbf{Pr = P(A) \times 60\%}[/tex]

Substitute 55% for P(A)

[tex]\mathbf{Pr = 55\%\times 60\%}[/tex]

Multiply

[tex]\mathbf{Pr = 0.33}[/tex]

Express as percentage

[tex]\mathbf{Pr = 33\%}[/tex]

Hence, the probability is 33%

Read more about probabilities at:

https://brainly.com/question/10837034

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