Question

Consider the following variant of question 3. If Z~n−1​=j, then first set Yn​=Xn−1,1​+⋯+Xn−1,​ where the random variables Xn−1,ℓ​ are independent of.

Answer 1

The given question asks to find the probability of a certain event using the basic addition rule and knowledge that the events are independent.

Step-by-step explanation:

The given question is related to the concept of independent events in probability theory.

1. To determine the probability of the union of two independent events, we can use the formula P(Y OR Z) = P(Y) + P(Z) - P(Y AND Z).
2. Since Y and Z are independent, P(Y AND Z) = P(Y) * P(Z).
3. For the given values P(Y OR Z) = 0.71 and P(Y) = 0.42, we can use the formula to find P(Z) as follows:
   P(Y OR Z) = P(Y) + P(Z) - P(Y) * P(Z)
   0.71 = 0.42 + P(Z) - 0.42 * P(Z)
   P(Z) = 0.71 - 0.42 + 0.42 * P(Z)
   P(Z) = 0.29 + 0.42 * P(Z)