Final answer:
The question asks for the expression of three probabilities involving the passing probabilities of Nik, Arif, and Ryan. To calculate these probabilities, use the multiplication rule and the addition rule of probability.
Step-by-step explanation:
The question is asking for the expression of the three probabilities a., b., and c., which involve the probabilities of Nik, Arif, and Ryan passing. To calculate these probabilities, we can use the multiplication rule and the addition rule of probability.
a. (P(Nik) * (1 - P(Arif)) * (1 - P(Ryan))
b. (1 - P(Nik)) * (P(Arif)) * (1 - P(Ryan))
c. (1 - (1 - P(Nik))) * (1 - P(Arif)) * (1 - P(Ryan))
According to the multiplication rule, if we want to find the probability of two independent events A and B occurring together (denoted as P(A AND B)), we multiply their individual probabilities: P(A AND B) = P(A) × P(B).
The addition rule assists in finding the probability of either event A or event B occurring (denoted as P(A OR B)). It states that this is equal to the sum of the individual probabilities minus the probability that both happen together: P(A OR B) = P(A) + P(B) - P(A AND B).