Avis

In: Business and Management

Submitted By diakyasmine
Words 1322
Pages 6
Homework Assignment One Solutions
Probability and Probability Distributions

1. A two-sided coin is flipped twice. Calculate the probability of: a. A head on the first flip (1 point) P(H) = [pic]= 0.5 b. A tail on the second flip given that the first flip was a head (1 point) P(T | H) = P(T) = [pic]= 0.5 c. A tail on the first flip and a head on the second flip (1 point) P(TH) = P(T) ( P(H) = (0.5)(0.5) = 0.25 d. At least one head on the two flips (1 point) At least one head means that we observe either HT, TH, or HH. Since each of these outcomes has a probability of 0.25, the probability of one of these three outcomes occurring is P(HT) + P(TH) + P(HH) = 0.25 + 0.25 + 0.25 = 0.75. An alternative means for determining the probability of observing at least one head in two flips would be to calculate the complement of the probability of observing two tails in two flips, which is the only possible outcome that does not include at least one head. P(TT) = 0.25, thus the complement of P(TT) = 1 – 0.25 = 0.75.

2. In a sample of 1,000 representing a survey from the entire population, 650 people were from Laketown, and the rest of the people were from River City. Out of the sample, 19 people had some form of cancer. Thirteen of these people were from Laketown. a. Are the events of living in Laketown and having cancer independent, and why? (1 point) P(cancer | Laketown) = [pic]= 0.02 P(cancer) = [pic]= 0.019 The two events are not independent due to the fact that the probability of a person from Laketown having cancer is not the same as the probability of a person having cancer. b. Which city would you prefer to live in, assuming your objective is to avoid having cancer, and why? (1 point) P(cancer | River City) = [pic]= 0.017 I would prefer to…...

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