3 .100 women use a new pregnancy test, 44 of the women are actually pregnant. Of

Question

3 .100 women use a new pregnancy test, 44 of the women are actually pregnant. Of the women who are pregnant, 35 test positive. Of the women who are not pregnant, 8 of them test positive. Draw tree diagram and Calculate the probability for each event.

1.A randomly selected test is negative, given the woman is not pregnant

2.A randomly selected test is positive

3.A randomly selected test is from a woman who is pregnant given it is negative

4.A randomly selected test is incorrect (false-positive or false-negative)

4 .Fiction Cruiseline offers three ways to exercise on their cruise ships. 73 of the 86 passengers participated in at least one method of exercise. 36 people went rock climbing, 44 people went ice skating, and 19 went to the fitness center. 14 people went rock climbing and ice skating, 11 people went rock climbing and to the fitness center, and 9 people went ice skating and to the fitness center. 8 participated in all 3 exercises.   Calculate the probability for each given event.

1.A randomly selected passenger went rock climbing, given they did not go ice skating

2.A randomly selected passenger did not go rock climbing, given they did not go to the fitness center

3.A randomly selected passenger did not go ice skating, given they did at least two activities

Explanation / Answer

ANS 3)

Let A show the event that women is essentially positive and B shows the event that woman is not essentially pregnant. Let P show the event that test gives positive outcome and N shows the event that test gives negative result.

P (A) = 44 /100 =0.44 and since 100 -44 =56 women are not pregnant so

P (B) = 56 /100 = 0.56 And we have following conditional probability

P (P/A) = 35/44

P (P/B) = 8/ 56

1) By the complement rule we have

   P (N/ B) = 1 - P (P/B) = 1 - 8/56 = 48/ 56= 0.8571

2) By the law of total probability, the probability that test is positive is

   P (P) = P (P/ B) P (B) + P (P/A) P (A) = (8/ 56)*(56/100) + (35/44) * (44/100) = 43/100 = 0.43

3) By the complement rule we have

P (N / A) = 1 - P (P/A) = 1 - 35/44 = 9/ 44 By the complement rule,

P (N) = 1 - P (P) = 0.57

   So the probability that a randomly selected test is from a woman who is pregnant given it is negtive is

    P (A/N) = [P (N/A) P (A)] / P (N) = [(9/44)*(44/100)] / 0.57 = 0.1579

4) P (N|A) + P (P|B) = 9/44 + 8/ 56 = 0.3474

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.