Use the following information to answer questions the lollowing table shows the

Question

Use the following information to answer questions the lollowing table shows the grade distribution of a class along with the gender of students. 8-16. emale Total 9 12 Male 0 10 4 15 Total 25 8) What is the probability that a randomly selected student is a Female? 9) What is the probability that a randomly selected student is a male and received a B? 10) A randomly selected student out turns out to be a male. Compute the probability that he received an A. 11) What is the probability that a randomly selected student received an A? 12) What is the probability that a randomly selected student received an A and B? 13) What is the probability that a randomly selected student received an A 0.B7 14) Given that the randomly selected student out turns out to be a male What is the probability that h received an A or B. 15) What is the probability that a randomly selected student received an A or is Female? 1o 1s reeiving an A indee eof iy k

Explanation / Answer

8) P(female ) = Number of females / Total number of students = 10/25 = 0.4

9) P(male and B ) = Number of males who received B / Total number of students = 8/25 = 0.32

10) P(male recived A ) = Male who received A / Total number of males = 3/15 = 0.20

11) P(Student received A ) = Students who received A / total number of students = 9/25 = 0.36

12) P(Student received A and B ) = 0 (Since a student can get only one grade)

13)P(Student received A or B ) = Students who received A + students who received B / total number of students = 12+9 / 25 = 21/25 = 0.84

14)  P(male recived A or B ) = Male who received A + male who received B / Total number of males = 11/15 = 0.73

15) P ( student got A or is a female ) = (student got A ) + (student is female ) - (females who got A ) / Total number of students

= 9+10 - 6 / 25 = 13/25 = 0.52

16) P(getting an A) = 9/25 (from 11 )

P(female ) = 10/25 (from 8 )

P (female and A ) = 6/25

P(getting an A) *   P(female ) = 9/25 * 10/25 = 90 / 625 = 0.144 which is not equal to  P (female and A ) = 6/25 = 0.24

Hence it is not independent.

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