Yesterday, 100 cars entered the Lakehead parking lot between 8:00 and 9:00 in th

Question

Yesterday, 100 cars entered the Lakehead parking lot between 8:00 and 9:00 in the morning. 29 of the cars were red, 17 had bumper stickers, 23 had fuzzy dice hanging from the mirrors, 10 were red cars with bumper stickers, 12 were red cars with fuzzy dice, 6 cars had bumper stickers and fuzzy dice and 2 were red cars having bumper stickers and fuzzy dice. (As usual, when we say, for instance, that 12 cars were red with fuzzy dice, that number includes the 2 that also had bumper stickers.) (a) Find the probability that a randomly selected car had a bumper sticker, but was not red. (b) Given that a randomly selected car was red, find the probability that it did not have a bumper sticker. (c) Given that a randomly selected car did not have a bumper sticker, find the probability that it did not have fuzzy dice.

Explanation / Answer

a) P(Car had a bumper sticker and not Red) = P(Bumper Sticker) - P(card had a bumper sticker and red)

= 17/100 - 10/100 = 7/100= 0.07

b) P(not bumer sticker / red car) = P(not bumper sticker and red car) / P(red car)

= [ P(red car) - P(bumper sticker and red car) ] / P(red car)

= [ 29/100 - 10/100] / [29/100] = [19/100] / [29/100] = 19/29 = 0.65517

c) P(not fuzzy dice / not bumper sticker] = P(not fuzzy dice and not bumper sticker) / P(not bumper sticker)

Now

P(not fuzzy dice and not bumper sticker) = 1 - P(fuzz dice and bumper sticker)

= 1 - P(fuzz dice) - P(bumper sticker) + P(fuzz dice and bumper sticker)

= 1 - (23/100) - (17/100) + (6/100) = 76/100= 0.76

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

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