Question

The table below lists a random sample of 50 speeding tickets on I-25 in Colorado.

	0-10 mph over limit	10-20 mph over limit	More than 20 mph over limit	Total
Male	9	9	17	35
Female	2	9	4	15
Total	11	18	21	50

Round to the fourth.
a) If a random ticket was selected, what would be the probability that the driver was female?
b) Given that a particular ticket had a male offender, what is the probability that they were more than 20 mph over the limit?
c) Given that a particular ticket was 10-20 mph over the limit, what is the probability that the driver was female?
d) If a random ticket was selected, what would be the probability that the driver was a male?
e) If a random ticket was selected, what would be the probability that the driver is a female and driving 10-20 mph over the limit?
f) If a random ticket was selected, what would be the probability that the driver is a female or driving 0-10 mph over the limit?

Answer 1

We are given a table:

	0-10 mph over limit	10-20 mph over limit	More than 20 mph over limit	Total
Male	9	9	17	35
Female	2	9	4	15
Total	11	18	21	50

(a) We have to find a probability that the driver was female:

so, favorable outcome = 15, which is total number of female

out of total drivers which is 50

so required probability =

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(b) We are given that a particular ticket had a male offender,

then probability that they were more than 20 mph over the limit:

i.e.

so,we get:

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(c) We are given that a particular ticket was 10-20 mph over the limit,

then the probability that the driver was female=

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(d)

We have to find a probability that the driver was male:

so, favorable outcome = 35, which is total number of male

out of total drivers which is 50

so required probability =

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(e) We have to find the  probability that the driver is a female and driving 10-20 mph over the limit:

so favorable outcome that it is female as well as 10-20 mph (its intersection would be 9) selected out of total drivers which is 50

so, required probability =

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(f) We have to find the probability that the driver is a female or driving 0-10 mph over the limit:

so, favorable outcome that it is female or 0-10 mph (its union would be sum of its values, which is 2+9+4+9= 24) selected out of total drivers which is 50.

so, required probability =

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