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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 ?
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Explanation :
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 = 5/26
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
A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?
Explanation
From 1 to 24, there are 8 numbers which are multiple of 3
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
8C2*16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253
Add both cases.
A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?
Explanation:
Total balls = 15
Not red means green or blue i.e. any of (5+6) = 11 balls
So prob. = 11C2 / 15C2
From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or heart card?
Prob. of black card:
26C2 / 52C2 = 25/102
Prob. of heart card:
13C2 / 52C2 = 3/51
From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children?
Case 1: Prob. when 2 men, 1 woman and 1 child
3C2*4C1*2C1 /9C4 = 4/21
Case 2: Prob. when 1 man, 2 women and 1 child
3C1*4C2*2C1 /9C4 = 2/7
Case 3: Prob. when 1 man, 1 woman and 2 children
3C1*4C1*2C2 /9C4 = 2/21
A box contains 25 bulbs out of which 5 are defective. 3 bulbs are to be delivered to a customer. What is the probability that he get one defective bulb?
5C1*20C2/25C3
There are 4 red balls, 5 white and 3 green balls in a basket. 3 balls are chosen at random. What is the probability that there is at most 1 green ball?
Case 1: 0 green ball means all three red or white balls
9C3/12C3
Case 2: 1 green ball and two red or white balls
9C2*3C1/12C3
A bag contains 3 red, 4 green and 3 yellow balls. If 2 balls are drawn at random, what is the probability that they are of different color?
This will be = 1- prob.(both are same in color)
Prob. of both same in color = [3C2+4C2+3C2]/10C2 = 12/45
So required prob. = 1 – 12/45
There are 4 black balls and 6 white balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are same in color?
When both black, prob. = 4/10 * 3/9
When both white, prob. = 6/10 * 5/9
A bag contains 5 red balls and 4 green balls. What is the probability that both balls are same in color?
Case 1: both red
5C2/9C2
Case 2: both green
4C2/9C2
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