The probability that Salim passes his math test is 0.45 and the probability that Latika passes her math test is 0.5

Quantity A

The probability that Salim passes his math test or Latika passes her math test or BOTH pass their math test

Quantity B

.45+.55-(.45)(.55).45+.55−(.45)(.55)

How is the the answer C. Quantity A equals 1 right?.

No, because it is possible that both fail their test.

Can you elaborate please. Do we need to subtract the probability that both fail?.

Yes, but both pass the test instead. Recall the formula from the Math Review: A \cup B = A + B - A \cap B . You want to find A \cup B after all.

A is the probability that Salim passes the test and B is Latika passes the test. P(A and B) is 0.45*0.55.
Why do we include the probability that both fail?

anesh1174014:

P(A and B) is 0.45*0.55.

That’s the probability of both passing. We are not looking at the probability of both failing.

I am sorry, I am still not gettin it.

P(a)+p(b)+p(a and b)= 0.45+0.55-(0.450.55) + (0.45 0.55)=1.

Why is the answer C?.

Please use Latex.

I don’t know why you’re adding 0.45 \times 0.55 though. P(A) = 0.45, P(B) = 0.55, P(A \cap B) = 0.45 \times 0.55 .

They ask for the probability that Salim passes the test OR Latika passes the test OR both pass the test.

P(A)+P(B)-P(A and B) gives the probability that Salim passes the test OR Latika passes the test

what about the probability that BOTH passes the test?

anesh1174014:

BOTH passes the test

It says OR both passes the test. That is literally A \cup B .