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Probability

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A businessman has an important meeting to attend, but he is running a little late. He can take one route to work that has six stoplights or another, longer route that has two stoplights. He figures that if he stops at more than half of the lights on either route, he will be late for the meeting. Assume independence, and assume that the chance of stopping at each light is p =0.5. Which route should he take?

It is claimed that for a particular lottery, 1/10 of the 50 million tickets will win a prize. What is the probability of winning at least one prize if you purchase (a) 10 tickets or (b) 15 tickets?

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Solution Summary

The solution contains several probability problems using Binomial distribution.

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Solution 4-15

a) Let X denote the number of prizes won if 10 tickets were purchased. Here it is given that the probability of winning a prize is 1/10 = 0.10. Clearly X follows a Binomial distribution with parameter n = 10 and p = 0.10. Thus the p.m.f. of X is given by,
, x = 0, 1, 2, 3,..., 10.
Now, the probability of winning at least one prize is given by,

= 1 - 0.3487
= 0.6513

b) Let X denote the number of prizes won if 15 tickets were purchased. Here it is given that the probability of winning a prize is 0.10. Clearly X follows a Binomial distribution with parameter n = 15 and p = 0.10. Thus the p.m.f. of X is given by,
, x = 0, 1, 2, 3,..., 15.
Now, the probability of winning at least one prize is given by,

= 1 - 0.2059
= 0.7941

Solution 4-16

Let n denote the number of tickets purchased and ...

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