Given events J and K: P(J ) = 0.19; P(K ) = 0.31; P(J OR K ) = 0.44.

Question

Given events J and K: P(J ) = 0.19; P(K ) = 0.31; P(J OR K ) = 0.44.

Part (a)

Find P(J AND K ). (Enter an exact number as an integer, fraction, or decimal.)

Part (b)

Find the probability of the complement of event (J AND K ). (Enter an exact number as an integer, fraction, or decimal.)

Part (c)

Find the probability of the complement of event (J OR K ). (Enter an exact number as an integer, fraction, or decimal.)

Answer 1

We can use the general addition rule to find P(J and K). The general addition rule for 2 events J and K is

P(J or K) = P(J) + P(K) - P(J and K). Substituting in the given numbers:

0.44 = 0.19 + 0.31 - P(J and K). Solving for P(J and K):

-0.06 = -P(J and K) or P(J and K) = 0.06.