Question

A student is taking two courses, history and math. The probability the student will pass the history course is .54, and the probability of passing the math course is .61. The probability of passing both is .43. What is the probability of passing at least one

Answer 1

The probability of passing at least one is:

0.72

Explanation:

Let A denote the event that the student passed in history subject.

Let B denote the event that the student passed in math subject.

Then A∪B denote the event that he passed in atleast one.

A∩B denote the event that he passed in both.

We know that:

`P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)`

From the ques we have:

`P(A)=0.54\\\\P(B)=0.61\\\\and\\\\P(A\bigcap B)=0.43`

Hence, we get:

`P(A\bigcup B)=0.54+0.61-0.43\\\\P(A\bigcup B)=0.72`

Hence, the answer is:

0.72