IIT JEE , AIEEE Forum - Mathematics , Algebra

babanbanerjee

Sum on Probability2

::::::::::::

There are 3 groups.The 1st group contains 3 girls & and 1 boy.The 2nd group contains 2girls and 2 boys whereas the 3rd contain 1girl and 3 boys.Another group is formed by picking one student from the existing groups.What is the probability that the goup formed will contain 1 boy & 2 girls.

babanbanerjee

Rates assured.Plz reply.

rudra.panda

is the answer 13/32?

rudra.panda

Group #1 - 3G, B

Group #2 - 2G, 2B

Group #3 - G, 3B

1) Boy comes from #1, and the girls come from #2 and #3.

$\frac{1}{4}\times \frac{1}{2} \times \frac{1}{4}=\frac{1}{32}$

2) Boy comes from #2, and the girls come from #1 and #3.

$\frac{3}{4}\times\frac{1}{2}\times\frac{1}{4}=\frac{3}{32}$

3) Boy comes from #3, and the girls come from #1 and #2.

$\frac{3}{4}\times\frac{1}{2}\times\frac{3}{4}=\frac{9}{32}$

$\frac{1}{32}+\frac{3}{32}+\frac{9}{32}=\frac{13}{32}$

answer : $\frac{13}{32}$

spideyunlimited

The 3 groups are A, B and C.
The prob. we have to find is of getting BGG where B is boy and G is girl.

Case 1 - boy is selected from A, and the girls from B and C.
prob. of BGG = 1/4*1/2*1/4 = 1/32

Case 2 - boy is selected from B, and girls from A and C.
prob. of BGG = 1/2*3/4*1/4 = 3/32

Case 3 - boy is selected from C, and girls from A and B.
prob. of BGG = 3/4*3/4*1/2 = 9/32

Total prob. = Sum of prob.= 1/32 + 3/32 + 9/32
= 13/32

shivam999

Group #1 - 3G, B

Group #2 - 2G, 2B

Group #3 - G, 3B

1) Boy comes from #1, and the girls come from #2 and #3.

$\frac{1}{4}\times \frac{1}{2} \times \frac{1}{4}=\frac{1}{32}$

2) Boy comes from #2, and the girls come from #1 and #3.

$\frac{3}{4}\times\frac{1}{2}\times\frac{1}{4}=\frac{3}{32}$

3) Boy comes from #3, and the girls come from #1 and #2.

$\frac{3}{4}\times\frac{1}{2}\times\frac{3}{4}=\frac{9}{32}$

$\frac{1}{32}+\frac{3}{32}+\frac{9}{32}=\frac{13}{32}$

answer : $\frac{13}{32}$

Ask & Discuss Questions with Community & Experts