Suppose a study of speeding violation and drivers who use car phones produced fi

Question

Suppose a study of speeding violation and drivers who use car phones produced fictional data: Suppose 9% of drivers have speeding violation in the last year and 40% of the drivers use car phones. Of the car phone users 8% have speeding violation in the last year. Let S be the event that a driver has a speeding violation in the last year. And let C be the event that a driver uses a car phone. a) Complete the contingency table Total b) Find P(S AND C). c) Find P(C|S). d) Find P(S OR C ). e) Using an appropriate test, show whether S and C are independent events. f) Using an appropriate test, show whether S and C are mutually exclusive events. g) Make a Venn diagram or a tree diagram of the situation.

total

Explanation / Answer

Here we have

P(S) = 0.09, P(C) = 0.40, P(S|C) = 0.08

So

P(S and C) = P(S|C)P(C) = 0.08 *0.40 = 0.032

(a)

Following is the completed table:

(b)

P(S and C) = P(S|C)P(C) = 0.08 *0.40 = 0.032

(c)

P(C|S) = P(C and S) / P(S) = 0.032 / 0.09 = 0.3556

(d)

By the addition rue we have

P(S or C) = P(S)+P(C)-P(S and C) = 0.09 +0.40 - 0.032 = 0.458

(e)

Since P(S and C) is not equal to P(S)P(C) so S and C are not independent.

(f)

No S and C are not mutually excluive because P(S and C) are not equal to zero.

Speeding violation Yes No Total Car phone users Yes 0.032 0.368 0.4 No 0.058 0.542 0.6 Total 0.09 0.91 1

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