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Additional Probability Problems. 1) The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest type AB. Someone volunteers to give blood, what is the probability that this donor has Type AB blood? has Type A or Type B?

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1) The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest type AB.

  • Someone volunteers to give blood, what is the probability that this donor
  • has Type AB blood?
  • has Type A or Type B?
  • has the complement of Type O?

4%

51%

55%

slide3

2) The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest type AB.

  • Among four potential donors, what is the probability that
  • all are Type O?
  • no one is Type AB?
  • at least one is Type B?
      • d) they are not all Type A?

0.041

0.849

0.373

0.974

slide4

3) A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired only once, another 7% need repairs twice, and another 4% will require three or more repairs.

  • If you own two cars, what is the probability that
  • neither will need repair?
  • both will need repair?

.5184

.0784

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4) A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and a bell. If you play, what is the probability

  • you get 3 lemons?
  • you get no fruit symbols?
  • you get 3 bells (the jackpot)?
  • you get no bells?
    • e) you get at least one bar (automatically lose)?

.027

.125

.001

.729

.784

slide6

5) Suppose the police operate a sobriety checkpoint after 9 p.m. on a Saturday night when national traffic experts suspect about 12% of drivers have been drinking. Trained officers can correctly decide if a person has been drinking 80% of the time. What’s the probability that

  • any given driver will be detained for drunk driving?
  • a driver who was detained has actually been drinking?
      • c) a driver who was released had actually been drinking?

.272

.353

.033