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A man buys a racehorse for ​$20,000 and enters it in two races. He plans to sell the horse​ afterward, hoping to make a profit. If the horse wins both​ races, its value will jump to ​$90,000. If it wins one of the​ races, it will be worth ​$55,000. If it loses both​ races, it will be worth only ​$15,000. The man believes there is a 30​% chance that the horse will win the first race and a 40​% chance that it will win the second one. Assuming that the two races are independent​ events, find the​ man's expected profit.

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ayfat23

Answer

$22400

Step by step Explanation

Cost of the racehorse = ​$20,000

value of racehorse if both races were won= ​$90,000

Value racehorse if one of the races were won=$55,000

Value of the racehorse if both​ races were lost= ​$15,000.

The probability of horse will win the first race is 0.30.

The probability that horse will win the second race is 0.40.

✓The probability of winning both the races is,

P(win both)= p(wining the first race) ×p(wining second race)

= 0.3×0.40

=0.12

√The probability of winning exactly one race is,

P(win one)= p(winning one race) p( not winning the other one)

0.3(1-0.4)+0.3(1-0.4)

=0.46

√The probability of losing both the races is,

[1-p(winning first race)] × [1-p(winning second race)]

=(1-0.4)(1-0.3)

=0.42

But we were to find the man’s expected profit, which can be calculated as;

[The probability of winning both the races×(value of racehorse if both races were won-Cost of the rracehorses)] +[The probability of winning exactly one race ×(Value racehorse if one of the races were won -Cost of the racehorse)] +[The probability of losing both the races ×(Value of the racehorse if both​ races were -cost of the race horse)]

0.12($90,000-$20,000)+0.46(55,000-20,000)+0.42(15,000-20,000)

=$22400

Therefore, the man’s expected profit is $22400

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