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Mac or PC? A recent census at a major university revealed that60%of its students mainly used 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 respondents were graduate students and used a Mac as their main computer. Suppose we select a student at random from among those who were part of the census. Define events G: is a graduate student and M: primarily uses a Mac.

a. Find P(G 鈭 M). Interpret this value in context.

b. Consider the event that the randomly selected student is an undergraduate student and

primarily uses a PC. Write this event in symbolic form and find its probability.

Short Answer

Expert verified

(a) The value of PGMis0.70.

(b) The symbolic form is PUPand the probability is0.30.

Step by step solution

01

Part (a) Step 1: Given Information

We are given the values of the students who are undergraduate and who use Macs and also those who are both graduate and use Macs, and we have to find out the probability of those who are either graduate or use Macs.

02

Part (a) Step 2: Explanation

Applying the union rule of probability

which isPAB=P(A)+P(B)+P(AB),

Here, P (G)=1-PU=1-0.67=0.33, P (M)=0.60and P(GM)=0.23

Put all the values in the rule.

We get PGM=0.33+0.60-0.23=0.70

Hence, the probability of those who are graduates or using Macs is0.70

03

Part (b) Step 1: Given Information

We are given the values of the students who are undergraduate and who use Macs and also those who are both graduate and use Macs, and we have to find out the probability of those who are graduate or use Macs.

04

Part (b) Step 2: Explanation

Applying the union rule of probability,

which isPAB=P(A)+P(B)+P(AB)

Here, the probability of students who are undergraduates and use primarily PCS is denoted by PUP. Now, to find its value,

P(U)=0.67, P(P)=1-P(M)=1-0.60=0.40

and P(UP)=1-0.23=0.77

Put all the values in the union rules.

we getPUP=0.67+0.40-0.77=0.30.

Hence, the probability is0.30.

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