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Chapter 5: Q 96. (page 331)

Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Macintosh computers (Macs). The rest mainly used

PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23%of the respondents were graduate students who said that they used PCs as their

primary computers. Suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a Mac.

Find the probability that this person is a graduate student. Show your work.

Short Answer

Expert verified

The probability that the person is a graduate student is 0.25

Step by step solution

01

Step 1. Given Information

A MAC is used by 40% of people. Undergraduates make up 67%of the group. Only 23% of grads use a computer exclusively.

02

Step 2. Concept used

Conditional probability: P(B|A)=P(AandB)/P(A)

03

Step 3. Calculation

Combining the above data to get the following two-way table, according to the question

Conditional probability: P(B|A)=P(AandB)/P(A)

Assess using the two-way table, as follows:

PGraduate/MAC)=P(GraduateandMAC)/P(MAC)

=10%40%=14=0.25

As a result, there is a 0.25chance that the person is a graduate student.

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Most popular questions from this chapter

Roulette, An American roulette wheel has38slots with numbers 1through 36,0,and00,as shown in the figure. Of the numbered slots, 18are red, 18are black, and 2鈥攖丑别 0and 00鈥攁re green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball

is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events B: ball lands in a black slot, and E: ball lands in an even numbered slot. (Treat 0and 00as even numbers.)

(a) Make a two-way table that displays the sample space in terms of events B and E.

(b) Find P(B) and P(E).

(c) Describe the event 鈥淏 and E鈥� in words. Then find P(B and E). Show your work.

(d) Explain why P(B or E) 鈮� P(B) + P(E). Then use the general addition rule to compute P(B or E).

Who eats breakfast? Refer to Exercise 68. Are events B and M independent? Justify your answer.

Construct a tree diagram to represent this situation.

Simulation blunders Explain what鈥檚 wrong with each of the following simulation designs.

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