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.

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

The Last One

Step-by-step explanation:

I used a special calculator plus, I did this already lol. Trust me <3