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A box contain 4 white, 3 blue and 2 black marbles. If 2 marbles are picked up at random. What is the probability that both of them are black ?
P = 2C2/9C2 = 1/36
An urn contains 6 maroon, 3 pink and 4 white balls. If three balls are drawn What is the probability that all are pink or white?
P =3C3/13C3 + 4C3/13C3
= 1/286 + 4/286 = 5/286
From a pack of 52 cards 3 cards are drawn one by one without replacements.Find the probability that both of them are king ?
4/52*3/51*2/50 = 24/132600 = 4/22100 = 1/5525
If two dice are thrown simultaneously, what is the probability that the sum of the numbers appeared is less than seven?
Sum of the numbers can be 1,2, 3, 4, 5, and 6.
1+2= 3
1+3 = 4
1+4 = 5
1+5 = 6
2+3 = 5
3+2 = 5
2+4 = 6
4+2 = 6……..etc
n (E) = 15, n (S) = 36
P (E) =15/36 = 5/12
A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marbles are drawn at random, what is the probability that both are green or at least one is green ?
4C2+(4C1*10C1)/12C2 = 6+40/91 = 46/91
In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. One book is picked up randomly. What is the probability that it is neither in Banking awareness nor in GK ?
P = 6/18 = 1/3
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?
P = 4C1*8C3/12C4 = 4*56/495 = 224/495
A bag contains 4 white, 8 black and 6 blue balls. If two balls are drawn at random, find the probability of both the balls being black?
n(S) = 18C2 = 153
There are eight black balls, out of which two balls are drawn in 8C2 ways.
n(E) = 28
P(E) = 28 /153 = 28/153
The ratio of the number of girls to the number of boys is the 5 : 2 in a class of 21 students. A group of three students is to to be selected at random amongst them. What is the probability that the selected group of students contain one boy and two girls?
5:2 = 15+6 = 21
n(S) = 21C3 = 1330
n(E) = 15C1 × 6C2 = 15 × 15 = 225
P = 225/1330 = 45/266
A bag 5 red and 8 white balls.Two draws of three balls each are made.What is the probability that the balls were pink in the first draw and white in the second draw ?
5C3/13C3 *8C3/13C3 = 60/286*56/286 = 140/20449
From a pack of 52 cads, 2 cards are drawn at random. What is the probability of drawing such that there is at least 1 king?
Case 1: 1 is king
^{4}C_{1} * ^{48}C_{1} / ^{52}C_{2}
Case 2: both are king
^{4}C_{2} / ^{52}C_{2}
Add both cases.
A box contains 6 blue, 5 green and 4 red balls. If two balls are pick at random, then what is the probability that neither is blue?
Total balls = 15
Not blue means green or red i.e. any of (5+4) = 9 balls
So prob. = ^{9}C_{2} / ^{15}C_{2}
A box contains 5 blue and 5 white balls. What is the probability of drawing 2 balls such that both are same in color?
Case 1: Both blue
^{5}C_{2} / ^{10}C_{2}
Case 2: Both white
^{5}C_{2} / ^{10}C_{2}
Add both cases
A committee of 4 people is to be formed from 3 men, 2 women and 4 children. What is the probability that exactly two of chosen people are children?
2 children should be there and rest 2 either from (2 women + 3 men) 5 people
So prob. = ^{4}C_{2} * ^{5}C_{2} / ^{9}C_{4}
In a class 30% of the students opt for Math, 20% opt for Computers and 10% opt for both. A student is selected at random, find the probability that he has opted either Math or Computers.
Prob. of math = 30/100 = 3/10, Prob. of computers = 20/100 = 1/5, prob. for both = 10/100 = 1/10
So required prob. = 3/5 + 1/5 – 1/10
From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?
Prob. of both red = ^{26}C_{2} / ^{52}C_{2}
Prob. of both kings = ^{4}C_{2} / ^{52}C_{2}
Since there are also cads which are both red and king, so we will subtract there prob.
There are 2 red cards which are kings
Prob. of both red and king = ^{2}C_{2} / ^{52}C_{2}
So required prob. = ^{26}C_{2} / ^{52}C_{2} + ^{4}C_{2} / ^{52}C_{2} – ^{2}C_{2} / ^{52}C_{2}
A box contains 10 electric bulbs from which 2 bulbs are defective. Two bulbs are chosen at random. What is the probability that one of them is defective?
A bag contains 8 blue and 7 green balls. A ball is drawn out of it and put back in the bag. Then a ball is drawn again. What is the probability that both the balls are green?
A bag contains 8 blue and 7 green balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are alternately of different colors?
When 1st is blue, prob. = 8/15 * 7/14
When 1st is green, prob. = 7/15 * 8/14
Add both cases.
There are 5 men and 3 women. A committee of 3 members is to be made. Find the probability that either there are 2 men and 1 woman or 2 women and 1 man.
2 men and 1 woman, prob. = ^{5}C_{2} * ^{3}C_{1} / ^{8}C_{3}
2 women and 1 man, prob. = ^{5}C_{1} * ^{3}C_{2} / ^{8}C_{3}
Add both cases
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