Discrete Probability 1 In a certain park in Singapore it cos

Discrete Probability

(1) In a certain park in Singapore, it costs $7 per day to park at the parking lot. A car that is illegally parked will be fined $25 if caught, and the chance of being caught is 60%. If money is the only concern for a person who must park at the location every day, should he park at the lot illegally?

(2) A fisherman catches fish at a Poisson rate of two per hour from a large lake with lots of fish. If he starts fishing at 10 AM, what is the probability that he catches one fish by 10.30 AM and three fish by 12 PM?

(3) In a school, 35% of a total of 560 students are left-handers. If, in a statistical survey, 15 students are randomly selected without replacement, what is the probability that at least two students are left-handers?

Solution

1.

If he pays, we automatically loses

E(x, legal) = -7.

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If he parks illegally,

Not caught: x1= 0, p1 = 0.4
Caught: x = -25, p2 = 0.6

Thus,

E(x) = p1 x1 + p2 x2 = (0.4)(0) + (0.6)(-25) = -15

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Thus, there is greater loss in illegal parking. THUS, HE SHOULD NOT PARK ILLEGALLY AND PAY INSTEAD.

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