at the beginning of the semester, a professor tells students that if they study for the tests, then there is…

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?\n0.08\n0.11\n0.33\n0.55

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?\n0.08\n0.11\n0.33\n0.55

Answer

Answer:

0.33

Explanation:

Step1: Define events

Let $S$ be the event that a student studies and $B$ be the event that a student gets a B or higher.

Step2: Identify given probabilities

We know $P(S)=0.6$, $P(B|S) = 0.55$.

Step3: Use multiplication rule

The multiplication rule for conditional - probability is $P(S\cap B)=P(B|S)\times P(S)$.

Step4: Calculate the probability

Substitute the values: $P(S\cap B)=0.55\times0.6 = 0.33$.