4.11 Probability topics: homework  (Page 5/6)

Suppose that 10,000 U.S. licensed drivers are randomly selected.

• a How many would you expect to be male?
• b Using the table or tree diagram from the previous exercise, construct a contingency table of gender versus age group.
• c Using the contingency table, find the probability that out of the age 20 - 64 group, a randomly selected driver is female.

Approximately 86.5% of Americans commute to work by car, truck or van. Out of that group, 84.6% drive alone and 15.4% drive in a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation. ( Source: Bureau of the Census, U.S. Dept. of Commerce. Disregard rounding approximations. )

• a Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.
• b Assuming that the walkers walk alone, what percent of all commuters travel alone to work?
• c Suppose that 1000 workers are randomly selected. How many would you expect to travel alone to work?
• d Suppose that 1000 workers are randomly selected. How many would you expect to drive in a carpool?

Explain what is wrong with the following statements. Use complete sentences.

• a If there’s a 60% chance of rain on Saturday and a 70% chance of rain on Sunday, then there’s a 130% chance of rain over the weekend.
• b The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit.

Find $\text{P(tossing a Head on the coin AND a Red bead)}$

• A $\frac{2}{3}$
• B $\frac{5}{\text{15}}$
• C $\frac{6}{\text{36}}$
• D $\frac{5}{\text{36}}$

Find $\text{P(Blue bead)}$ .

• A $\frac{\text{15}}{\text{36}}$
• B $\frac{\text{10}}{\text{36}}$
• C $\frac{\text{10}}{\text{12}}$
• D $\frac{6}{\text{36}}$

Find $\text{P(hit was made by Babe Ruth)}$ .

• A $\frac{\text{1518}}{\text{2873}}$
• B $\frac{\text{2873}}{\text{12351}}$
• C $\frac{\text{583}}{\text{12351}}$
• D $\frac{\text{4189}}{\text{12351}}$

Find $\text{P(hit was made by Ty Cobb | The hit was a Home Run)}$

• A $\frac{\text{4189}}{\text{12351}}$
• B $\frac{\text{114}}{\text{1720}}$
• C $\frac{\text{1720}}{\text{4189}}$
• D $\frac{\text{114}}{\text{12351}}$

Are $\text{the hit being made by Hank Aaron}$ and $\text{the hit being a double}$ independent events?

• A Yes, because $\text{P(hit by Hank Aaron | hit is a double) = P(hit by Hank Aaron)}$
• B No, because $\text{P(hit by Hank Aaron | hit is a double) ≠ P(hit is a double)}$
• C No, because $\text{P(hit is by Hank Aaron | hit is a double) ≠ P(hit by Hank Aaron)}$
• D Yes, because $\text{P(hit is by Hank Aaron | hit is a double) = P(hit is a double)}$

Given events G and H: P(G) = 0.43 ; P(H) = 0.26 ; P(H and G) = 0.14

• A Find P(H or G)
• B Find the probability of the complement of event (H and G)
• C Find the probability of the complement of event (H or G)