lexis wrote:

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?

(1) There are 50 male students in the class.

(2) The probability of selecting one male and one female student is 21/50.

A Detailed ExplanationQuestion : probability that two male students or two female students are selected?Statement 1)There are 50 male students in the class.

Male = 50 But No. of Female Students is unknown therefore Probability can't be calculated

INSUFFICIENT

Statement 2) 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 selectedtherefore, 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 = 7probability 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 = 29/50

Case 2: male = 7 and female = 3probability 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

Answer: Option

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