rewrite the addition A. Rewrite the basic adition rule P(Y or Z) = P(Y) = P(Z) - P(Y and Z) using the information tha Y and Z are independent events.

Question

A. Rewrite the basic adition rule P(Y or Z) = P(Y) = P(Z) - P(Y and Z) using the information tha Y and Z are independent events.

B. Use the rewritten rule to find P(Z) if P(Y or Z) = 0.69 and P(Y)= 0.44

Answer 1

When the events are independent P(Y and Z)=P(Y)P(Z), so

A) P(Y or Z)=P(Y)+P(Z)-P(Y and Z)=P(Y)+P(Z)-P(Y)P(Z). Note that the second equals sign should have been +.

B) 0.69=0.44+P(Z)(1-0.44)=0.44+0.56P(Z), P(Z)=0.25/0.56=0.47 approx.