1. Five good fuses and two defectives ones are inadvertently mixed. To find the

Question

1. Five good fuses and two defectives ones are inadvertently mixed. To find the defective ones, each one is tested one-by-one. If the defective ones are identified only in the third attempt, what is the probability of that EVENT?

2. Two events A and B have probabilities respectively of p(A) and p(B). What is the probability that exactly one event will occur if (a) A and B are mutually exclusive (b) A and B are not mutually exclusive, but dependent (c) A and B are not mutually exclusive, but independent.

Explanation / Answer

1) probability that defective ones are identified only in the third attempt =first one is good*second one is good*third one is defective =(5/7)*(4/6)*(2/5)=0.1905

2)a)for mutually exclusive probability that exactly one event will occur =P(AUB)-P(A and B)

                                                            =P(A)+P(B)-P(A and B)-P(A and B)

                                                             =P(A)+P(B)-2*P(A and B)

                                                             =P(A)+P(B)-2*0 =P(A)+P(B)

b) for dependent events probability that exactly one event will occur = =P(A)+P(B)-2*P(A and B)

c) for independent events probability that exactly one event will occur = P(A)+P(B)-2*P(A and B)

                                    =P(A)+P(B)-2*P(A)P(B)

please revert for any clarification

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