# Homework Statistics Week 4

1. Section 3.1, Exercise #14, p. 125 Finding Probabilities consider a company that selects employees for random drug tests. The company uses a computer to select randomly employee numbers that range from 1 to 6296. Find the probability of selecting a number greater than 1000.

P(E) = Number of outcomes in E / Total number of Outcomes in sample space Number of outcomes in E = 6296 – 100 = 5296

The probability = P(E) = 5296 / 6296 = 0.841 = 84.1% There is an 84.1 percent probability of selecting a number greater than 1000 2. Section 3.1, Exercise #20, p. 126 Using a Frequency Distribution to Find Probabilities in use the frequency distribution, which shows the number of American voters (in millions) according to age.

18 to 20 years old 4.8

21 to 24 years old 7.3

25 to 34 years old 20.4

35 to 44 years old 28.4

45 to 64 years old 43.7

Find the probability that a voter chosen at random is between 35 and 44 years old.

Probability = 28.4 / (4.8 + 7.3 + 20.4 + 28.4 + 43.7 + 24.9) = 0.2193 = 21.93% 3. Section 3.2, Exercise #16, p. 136 A doctor gives a patient a 60% chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, he has a 50% chance that the heart damage will heal. Find the probability that the patient survives and the heart damage heals.

Let BS be the event that the patient survives bypass surgery. Let H be the event that the heart damage will heal.

Then P(BS) = 0.60, and also we have a conditional probability: given the patient survives the probability that the heart damage will heal is 0.5, that is P(H|BS) = 0.5 We want to know P(BS and H).

Using the formula of the conditional probability:

P(H and BS) = P(H|BS)·P(BS) = (0.6)(0.5) = 0.3

That is the probability that the patient survives and the heart damage...

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