Suppose E and G are independent events. Then P(E∪G)=____

May 2021 2 70 Report

Suppose E and G are independent events. Then P(E∪G)=_____?

In an experiment, the probabilities of the events E, F and G are known to be 0.500,0.150, and 0.220 respectively.

Suppose E and G are independent events. Then P(E∪G)=_____

If E and G are independent events, P(E ∩ G) = P(E) P(G)

P(E U G) = P(E)+P(G) - P(E ∩ G)

P(E U G) = P(E)+P(G) - P(E) P(G) = 0.500 +0.220 - (0.500)(0.220)

= .5+.22-.11 = 0.61

If E and G are independent, then the occurrence of E doesn't affect the probability of G and vice versa.

That is, P(E|G) = P(E) and P(G|E) = P(G).

P(E∩G) = P(E)P(G|E) (the multiplication rule), so this becomes

P(E∩G) = P(E)P(G)

P(E∩G) = P(E) + P(G) - P(E∪G) (the addition rule), which becomes

P(E)P(G) = P(E) + P(G) - P(E∪G)

This can be arranged for P(E∪G) = P(E) + P(G) - P(E)P(G).

So P(E∪G) = 0.500 + 0.220 - 0.500*0.220 = 0.61