If two students are chosen at randomwith replacementfrom a certain class, what is the probability that two male students or two female students are selected?A Detailed ExplanationQuestion : probability that two male students or two female students are selected?Statement 1)
(1) There are 50 male students in the class.
(2) The probability of selecting one male and one female student is 21/50.
There are 50 male students in the class.
Male = 50 But No. of Female Students is unknown therefore Probability can't be calculated
The probability of selecting one male and one female student is 21/50
i.e. (No. of Males/Male+female) x (No. of Female/Male+female)x2! = 21/50
BUT since we are calculating probability with replacement therefore Probability of a male selected = 1-probability of a female selected
therefore, If probability of one male selected = x
then probability of one female selected = 1-x
therefore, x(1-x)*2 = 21/50
i.e. x(1-x) = 21/100
i.e. x = 3/10 or x = 7/10
i.e. out of 10 students, Case 1: male = 3 and female = 7
probability of both male = (3/10)x(3/10) = 9/100
probability of both Female = (7/10)x(7/10) = 49/100
i.e. Probability of Both male or Both Female = (9/100)+(49/100) = 58/100 = 29/50Case 2: male = 7 and female = 3
probability of both Female = (3/10)x(3/10) = 9/100
probability of both Male = (7/10)x(7/10) = 49/100
i.e. Probability of Both male or Both Female = (9/100)+(49/100) = 58/100 = 29/50
Either way we get unique answer therefore, SUFFICIENT
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