The table below shows the number of male and female students enrolled in nursing
ID: 2947370 • Letter: T
Question
The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester. (a) Find the probability that a randomly selected student is male, given that the student is a nursing major. (b) Find the probability that a randomly selected student is a nursing major, given that the student is male. Males Females Total Nursing Majors 96 724 820 Non-nursing majors 1060 1692 2752 Total 1156 2416 3572 (a) Find the probability that a randomly selected student is male, given that the student is a nursing major The probability is Round to three decimal places as needed.)Explanation / Answer
Solution :
To represent as N = Random student is a Nursing major
and M = Random student is a Male
=> P(M|N) => probability that random student is a male given that student is nursing major
=> P(M and N) => probability that random student is male and nursing student.
Formula : P(M|N) = P(M and N)/P(N)
(a) probability that a random selected student is male, given that the student is a nursing major
=> P(male|nursing major) = (96/3572)/(820/3572)
= 96/820
= 0.117
(b) probability that a random selected student is nursing major, given that the student is a male
=> P(nursing major|male) = (96/3572)/(1156/3572)
= 96/1156
= 0.083
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Given that a coin is tossed then the probability of a tail is = 1/2
and a six-sided die is rolled then the probability of rolling a number greater than 4 is 2/6
{5,6}
=> P(tail and number > 4) = (1/2)*(2/6)
= 1/6
= 0.167
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