Question

The probability that a student takes calculus or is on scholarship is 0.85. The probability that a student is on scholarship is 0.61 and the probability that a student is taking calculus is 0.31. If a student is randomly chosen, find the probability that the student is taking calculus and is on scholarship.

Answer 1

Answer:

0.07

Step-by-step explanation:

According to the Question,

Let C denote the event that a student takes calculus & S denote the event that a student is on scholarship.

• Given, The probability that a student takes calculus or is on scholarship is 0.85 [P(C ∪ S)=0.85] . The probability that a student is on scholarship is 0.61 [P(S)=0.61] . and the probability that a student is taking calculus is 0.31 [P(C)=0.31] .

We have,

⇒P(C ∪ S)=0.85 , P(C)=0.31 , P(S)=0.61

We Know, P(C∩S) = P(C) + P(S) − P(C∪S)

Then, Put the Above Values in the Equation, we get

So, P(C∩S) = 0.31 + 0.61 - 0.85 ⇒ 0.07

• Thus, The probability that the student is taking calculus and is on scholarship is 0.07