Please show work step by step, thanks! Eight horses are entered in a race. You r

Question

Please show work step by step, thanks!

Eight horses are entered in a race. You randomly predict a particular order for the horses to finish. What is the probability that your prediction is correct? b) the shuffle feature is used to play the songs in random order. What is the probability that the first Beyonce song is the 4h song played? c) pregnant, of whom 95 are positive using the test. The company uses the pregnancy test on 100 other women who are known not to be pregnant, of whom 99 are negative using the test. The company anticipates that of the women who will use the pregnancy test kit, 10% will actually be pregnant. If a randomly selected woman tests negative, what is the probability that she is not pregnant (i.e., the predictive value negative of the test)? A particular iPod playlist contains 100 songs, 10 of which are by Beyonce. Suppose A drug company uses a new pregnancy test on 100 women who are known to be

Explanation / Answer

a)

total number of orders of 8 horses =8! =40320

hence P(prediction is correct )=1/40320

b)

P(fist Beyonce song is 4th) =P(first 3 are not Beyonce song and 4th is Beyonce song)

=(90/100)*(89/99)*(88/98)*(10/97)=0.0749

c)

P(negative test)=P(pregnant and negative test)+P(not pregnant and negative test)

=0.1*(1-95/100)+(1-0.1)*(99/100)=0.896

hence P(not pregnant given negative test)=P(not pregnant and negative test)/P(negative test)

=0.9*(99/100)/0.896 =0.99442

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