Probabilities Help?

The probability of two events happening together is the product of the individual probabilities.

This is why the probability of getting two heads in two coin flips is 1/4, it's (1/2)²

So we are given P(A) = 2/5

we are given P(A and B) = 3/10

Since: P(A and B) = P(A) * P(B), we can find P(B):

P(A and B) = P(A) * P(B)

3/10 = 2/5 * P(B)

(3/10)(5/2) = P(B)

15/20 = P(B)

3/4 = P(B)

And when you "not" the probability, you subtract it from 1, so:

P(not B) = 1/4

P(A) = P( A n ( B u B') .......... where B' = not B

P(A) = P(A n B ) + P( A n B')

P(A) = P(A n B) + P(A) * P(B')

2/5 = 3/10 + 2/5 P(B')

4 = 3 + 4P(B')

P(B') = 1/4

P(A and B) = P(A) * P(B)

3/10 = 2/5 * P(B)

P(B) = 3/4

P(not B) = 1 - P(B)

P(not B) = 1 - 3/4

P(not B) = 1/4

P(not B) = 0.25