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Question

In a second grade class containing 14 girls and 7 boys 2 students are selected at random to give out the math papers. What is the probability that both are girls?

A. (14X14)/(21X21)
B. (14X13)/(21X20)
C. (14X7)/(21X21)
D. (7X7)/(21X21)

Answer 1

It's B.

The probability of the first student being a girl is (14/21)... easy enough.
The probability of the second student being a girl is (13/20), because there are only 13 girls left of the 20 remaining students.

The probability of both events happening is (14/21)x(13/20) = (14x13)/(21x20)

Answer 2

This is an N-choose-R problem.

You have 21 students, how many ways can you pick 2?

21choose2 = 21! / (19!*2!)
where, for example, a 5! would be 5*4*3*2*1 etc.


The event of interest is to choose 2 girls.
With 14 girls, that's 14choose2 = 14! / (12! * 2!)

P(2 girls) = [# ways to choose 2 girls] / [# ways to choose 2 of any combo]

= (14choose2) / (21choose2)


=[14! / (12! * 2!)] / [21! / (19!*2!)]
=(14 * 13 ) / (21 * 20)

B


The algebra is:
(14choose2) / (21choose2)
=[14! / (12! * 2!)] * [(19!*2!) / 21!]
=(14! * 19! *2!) / (12! * 21! * 2! )
=(14! * 19!) / (12! * 21!)
=(14! / 12!) * (19! / 21!)
=(14 * 13) * (1 / 21 * 20)
=(14 * 13 ) / (21 * 20)

Answer 3

The chance the first person chosen is a girl is 14/21. (14 girls out of the 21 students.)

The chance the second is a girl, assuming the first one is, is 13/20. (13 remaining girls out of the 20 remaining students.)

The chance both things are true is therefore (14/21) x (13/20), and we multiply the fractions to get (14x13)/(21x20), which is choice B.

Of course, we really should reduce the fraction to 13/30, but apparently we don't need to to choose the right answer.

Hope that helps!

Answer 4

The chance that the first is a girl is 14 out of 21.
The chance that the second is a girl is 13 out of 20.

Thus, (14*13)/(21*20).

Answer 5

b is the answer .... there are a total of 21 students (14 girls, 7 boys)
picking the first is 14 girls out of 21 students 14 / 21
next is picking the second, so a girl is 1st (one less) and the total is 1 less (20) so 1st is (14 / 21) and second is ( 13 / 20)

Answer 6

Aristotle Winger Dr. Aristotle Winger gained his Ph. D on the age of 26 from Carnegie Mellon college in the realm of Mathematical Sciences. A graduate of the Howard college variety of 1998, he's way more beneficial than only a mathematician. He has been Professor of arithmetic at Emory and Henry college in Southwestern Virginia because the fall of 2004.

Answer 7

The chances are 2/3 x 2/3, or 4/9-- a little less than one-half.

Answer 8

option B 14c2/21c2

Answer 9

B

Answer 10

B...