Carcass wrote:

The table below shows the distribution of a group of 40 college students by gender and class.

Attachment:

#GREexcercise The table below shows the distribution.jpg

If one student is randomly selected from this group, ﬁnd the probability that the student chosen is

(a) not a junior

(b) a female or a sophomore

(c) a male sophomore or a female senior

\((a) \frac{21}{40} (b) \frac{7}{10} (c) \frac{9}{40}\)

Math Review

Question: 13

Page: 297

Difficulty: medium

Explanation::

A) Total number of students = 40and total number of juniors = 19

Hence the probability of not selecting a junior = \(\frac{19}{40}\)

B) Total number of female students = 22Total number of sophomore = 16

here we have to use the OR probability ( event A = female and event B = sophomore)

i.e P(A or B) = P(A) + P(B) - P( A & B)

or P(female or a sophomore) = \(\frac{22}{40} + \frac{16}{40}- \frac{10}{40} = \frac{28}{40} = \frac{7}{10}\)

since the two events are dependent, so P(A & B) = \(\frac{10}{40}\) as the sophomore is counted twice (male and female)

C) Total number of male sophomore = 6Total number of female senior = 3

Hence the probability ( using OR probability)of selecting a male sophomore or a female senior = \(\frac{6}{40} + \frac{3}{40} - 0 = \frac{9}{40}\)( since the two events are independent hence P (male sophomore & a female senior) = 0

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