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Chapter 3: 3.15 (page 190)

Helen plays basketball. For free throws, she makes the shot 75% of the time. Helen must now attempt two free throws. C = the event that Helen makes the first shot. P(C) = 0.75. D = the event Helen makes the second shot. P(D) = 0.75. The probability that Helen makes the second free throw given that she made the first is 0.85. What is the

probability that Helen makes both free throws?

Short Answer

Expert verified

Probability that Helen makes both free throws = 0.6375 or 63.75%

Step by step solution

01

Basic Concepts 

Probability (A given B) = Probability (A & B) / Probability (B)

Pr (A I B) = P (A 鈭� B) / P (B)

02

: 

Pr (C) ie first shot = 0.75 ; Pr (D) ie second shot = 0.75

Pr (D) ie second shot, given Pr (C) ie first shot = 0.85

Pr ( D I C ) = P (C 鈭� D) / P (D)

0.85 = P (C 鈭� D) / 0.75

P (C 鈭� D), ie Pr (C & D) = 0.85 x 0.75 = 0.6375

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Most popular questions from this chapter

In a basket ball arena

鈥� 70% of the fans are rooting for the home team.

鈥� 25% of the fans are wearing blue.

鈥� 20% of the fans are wearing blue and are rooting for the away team.

鈥� Of the fans rooting for the away team, 67% are wearing blue.

Let A be the event that a fan is rooting for the away team.

Let B be the event that a fan is wearing blue.

Are the events of rooting for the away team and wearing blue independent? Are they mutually exclusive?

After Rob Ford, the mayor of Toronto, announced his plans to cut budget costs in late 2011, the Forum Research polled 1,046people to measure the mayor鈥檚 popularity. Everyone polled expressed either approval or disapproval. These are the results their poll produced:

鈥� In early 2011,60percent of the population approved of Mayor Ford鈥檚 actions in office.

鈥� In mid-2011,57percent of the population approved of his actions.

鈥� In late 2011, the percentage of popular approval was measured at 42percent.

a. What is the sample size for this study?

b. What proportion in the poll disapproved of Mayor Ford, according to the results from late 2011?

c. How many people polled responded that they approved of Mayor Ford in late 2011?

d. What is the probability that a person supported Mayor Ford, based on the data collected in mid-2011?

e. What is the probability that a person supported Mayor Ford, based on the data collected in early 2011?

You have a fair, well-shuffled deck of 52 cards. It consists of four suits. The suits are clubs, diamonds, hearts and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit. Three cards are picked at random.

a. Suppose you know that the picked cards are Q of spades, K of hearts and Q of spades. Can you decide if the sampling was with or without replacement?

b. Suppose you know that the picked cards are Q of spades, K of hearts, and J of spades. Can you decide if the sampling was with or without replacement?

In a recent issue of the IEEE Spectrum, 84engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference.

a. Organize the data in a chart.

b. Find the median, the first quartile, and the third quartile.

c. Find the 65thpercentile.

d. Find the 10thpercentile.

e. Construct a box plot of the data.

f. The middle 50%of the conferences last from _______ days to _______ days.

g. Calculate the sample mean of days of engineering conferences.

h. Calculate the sample standard deviation of days of engineering conferences.

i. Find the mode.

j. If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.

k. Give two reasons why you think that three to five days seem to be popular lengths of engineering conferences.

Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data: Table 3.2.


Speeding violation in the last yearNo speeding violation in the last yearTotal
Uses cell phone while driving25280305
Does not use cell phone while driving45405450
Total70685755

The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and

685. Notice that 305 + 450 = 755 and 70 + 685 = 755.

Calculate the following probabilities using the table.

a. Find P(Driver is a cell phone user).

b. Find P(driver had no violation in the last year).

c. Find P(Driver had no violation in the last year AND was a cell phone user).

d. Find P(Driver is a cell phone user OR driver had no violation in the last year).

e. Find P(Driver is a cell phone user GIVEN driver had a violation in the last year).

f. Find P(Driver had no violation last year GIVEN driver was not a cell phone user)
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