Question

Use probability techniques to solve the following questions. (Be sure to show all work)

1 - Of all murder victims in 2010 whose relation to the offender was known, 28.8% were killed by a family member and 53% by an acquaintance. The rest were killed by a stranger. What is the probability that a randomly selected murder victim was killed by a stranger?

2 - In a recent survey, 15 people preferred milk, 27 people preferred coffee and 18 people preferred juice as their primary drink for breakfast. If a person is selected at random, find the probability that the person preferred juice as their primary drink.

3 - The probability that sue will live on campus and buy a new car is 0.34. If the probability that she will live on campus is 0.53, find the probability that she will buy a new car, given that she lives on campus.

4. - A new employee has a choice of 7 health care plans, 3 retirement plans and 2 different expense accounts. If a person selects one of each option, how many different options do they have?

5. A box contains 24 syringes, 4 of which are defective. If 4 are used, then what is the probability that at least one syringe is defective?

Answer 1

1. P(killed by family member) = 28.8 % = 0.288

P(killed by acquaintance) = 53% = 0.53

P(killed by stranger) = 1- 0.288 - 0.53 = 0.182

P(killed by stranger) = 0.182

2. People who prefer milk = 15

  People who prefer coffee = 27

People who prefer juice = 18

Total numbers = 60

P( person preferred juice) = 18 / 60 = 0.30

3. P(A/B) = P(A B) / P(B)

P(live on campus and buy a new car) = 0.34

P(live on campus ) = 0.53

P(buy a new car/ lives on the campus)  = 0.34 / 0.53 = 0.642

  P(buy a new car/ lives on the campus) = 0.642

4. Different options = ₇C₁ * ₃C₁ * ₂C₁ = 7 * 3* 2 = 42

5. P(defective) = 4/24

n= 4

P(atleast one is defective ) = P(1) + P(2) +P(3) +P(4) = 1 - P(0)

P(atleast one is defective ) = 1- 0.482 = 0.518