Statistics

Question

7. Consider a variation on the “random ice cream price” (pay what you roll) process: Two fair, six sided dice are rolled, but now the price is the smaller number followed by the larger number.

 

a. Determine the probability that you can afford the ice cream cone if you only have 25 cents.

Explain/justify your answer (here and throughout).

b. Determine the probability that the price is an odd number.

8. Consider another variation on the “random ice cream price” process: Two dice are rolled, but now these are 10-sided dice with the digits 0 – 9 on the sides. The price is back to being the larger number followed by the smaller number.

a. Determine the probability that the price is no more than 10 cents.

b. Determine the probability that the price is more than 50 cents.

 

 

9. Consider yet another variation on the “random ice cream price” process: Three fair, six sided dice are rolled, and the price is the largest number followed by the smallest number. If you are the customer and therefore prefer a smaller price, would you prefer to use two dice or three dice, or would you not have a preference? Explain your answer, but do not bother to perform any calculations.

 

10. Suppose that you encounter two traffic lights on your commute to school. Based on past experience, you judge that the probability is .45 that the first light will be red when you get to it, .35 that the second light will be red, and .25 that both lights will be red.

a. Produce a probability table to organize the given probabilities.

b. Determine the probability that at least one light will be red. Also name the relevant probability rule that you could use.

c. Determine the long-run percentage of days for which neither light will be red.

 

11. Consider that the 2012 U.S. Pet Ownership and Demographics Sourcebook reports that 36.5% of American households have a pet dog and 30.4% have a pet cat.

a. Does it follow from this information that 66.9% (the sum of 36.5% and 30.4%) of American households have a pet dog or a pet cat? Explain/justify your answer.

b. Based on the information given, what is the smallest possible value for the percentage of American households that have a pet dog or a pet cat?

Answer 1

7a.

	1	2	3	4	5	6
1	Y odd	Y	Y odd	Y	Y odd	Y
2	Y odd	Y	Y odd	Y	Y odd	N
3	Y odd	Y	N odd	N	N odd	N
4	Y odd	Y	N odd	N	N odd	N
5	Y odd	Y	N odd	N	N odd	N
6	Y odd	N	N odd	N	N odd	N

The above table shows all 36 double roll outcomes. Cells marked with Y are combinations corresponding to ice cream prices of 25c or lower, according to the given rule. There are 18 Y’s out of 36 possible outcomes, so the probability is 18/36=1/2.

7b.

Assuming that we are looking for affordable prices that are also odd, we need to count the cells containing Y odd. There are 10 cells, so the probability is 10/36=5/18.

 

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