The probabilities are 0.4, 0.2, 0.3 and 0.1, respectively, that a delegate to a

Question

The probabilities are 0.4, 0.2, 0.3 and 0.1, respectively, that a delegate to a certain convention arrived by air, bus, automobile, or train.

a. Consider 12 randomly selected delegates at this convention. What is the probability that from these 12 delegates, 3 arrived by air, 3 arrived by bus, 3 arrived by automobile, and 3 arrived by train?

b. What is the probability distribution of X: the number of delegates that arrive until the first one arrives by train, inclusive. What is the probability that the 10th delegate that arrives, was the first one to arrive by train?

Explanation / Answer

a)from multinomial distribution probabilty =(12!/(3!*3!*3!*3!))*(0.4)3*(0.2)3*(0.3)3(0.1)3 =0.0051

b) X would have geometric distribution:

probability that the 10th delegate that arrives, was the first one to arrive by train =first 9 will not arrive by train*10th one arrive by train

=(1-0.1)9*0.1 =0.0387

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.