Question

in a bag containing 3 black balls and 2 red balls , a ball is picked at random then replaced. A second ball is chosen.
What is the probability of :

I. both balls being black II.one is black ,the other is red.


2.in a class of 22 boys and 18 girls , two students are to be selected .
What is the probability of selecting two students of the same sex.​

Answer 1

#1

3 black and 2 red balls, total number is 5

i) Both balls are black:

• P(BB) = 3/5*3/5 = 9/25

ii) Black and red balls:

• P(BR) = 2/5*3/5 = 6/25

#2

22 boys and 18 girls, total number is 40

Combinations of 2 students:

• 40C2 = 40!/38!2! = 40*39/2 = 780

Combination of 2 boys:

• 22C2 = 22!/20!2! = 22*21/2 = 231

Combination of 2 girls:

• 18C2 = 18!/16!2! = 18*17/2 = 153

Probability of selecting 2 students of the same sex:

• P(BB or GG) =
• (231 + 153)/780 =
• 384/780 =
• 96/195 ≈ 0.4923 = 49.23%