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A bag contains 5 red and 7 white balls. Four balls are drawn out one by one and not replaced. What is the probability that they are alternatively of different colours?
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Explanation :
Balls are picked in two manners – RWRW or WRWR
So probability = (5/12)*(7/11)*(4/10)*(6/9) + (7/12)*(5/11)*(6/10)*(4/9) = 14/99
P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?
Fix the position of P, then Q can be sit in 12 positions, so total possible outcome = 12
Now, exactly 4 persons are sitting between them. This can be done in two ways as shown in figure, so favourable outcomes = 2
So, probability = 2/12 = 1/6
10 persons are seated around a round table. What is the probability that 4 particular persons are always seated together?
Total outcomes = (10 -1)! = 9!
Favourable outcomes = 6!*4! (4 person seated together and 6 other persons seated randomly, so they will sit in (7-1)! Ways and those 4 persons can be arranged
in 4! ways)
So probability = 1/21
A box contains 4 red, 5 black and 6 green balls. 3 balls are drawn at random. What is the probability that all the balls are of same colour?
(4c3 + 5c3 + 6c3)/15c3 = 34/455
An apartment has 8 floors. An elevator starts with 4 passengers and stops at 8 floors of the apartment. What is the probability that all passengers travels to different floors?
Total outcomes = 8*8*8*8
Favourable outcomes = 8*7*6*5 (first person having 8 choices, after that second person have 7 choices and so on)
So, probability = 105/256
A speak truth in 60% cases and B in 80% cases. In what percent of cases they likely to contradict each other narrating the same incident?
P(A) = 3/5 and P(B) = 4/5. Now they are contradicting means one is telling truth and other telling the lie. So,
Probability = (3/5)*(1/5) + (2/5)*(4/5)
A box contains 30 electric bulbs, out of which 8 are defective. Four bulbs are chosen at random from this box. Find the probability that at least one of them is defective?
1 – 22c4/30c4 = 1 – 209/783 = 574/783
Two person A and B appear in an interview. The probability of A’s selection is 1/5 and the probability of B’s selection is 2/7. What is the probability that only one of them is selected?
A selects and B rejects + B selects and A rejects = (1/5)*(5/7) + (4/5)*(2/7) = 13/35
A 4- digit number is formed by the digits 0, 1, 2, 5 and 8 without repetition. Find the probability that the number is divisible by 5.
Total possibility = 5*4*3*2
Favourable outcomes = 2*4*3*2 (to be divisible by 5 unit digit can be filled with only 0 or 5, so only two possibilities are there, then the remaining can be filled in
4, 3 and 2 ways respectively)
so probability = 2/5
A bag contains 6 red balls and 8 green balls. 2 balls are drawn at random one by one with replacement. Find the probability that both the balls are green:
(8c1)/(14c1) * (8c1)*(14c1) = 16/49
A box contains 27 marbles some are blue and others are green. If a marble is drawn at random from the box, the probability that it is blue is 1/3. Then how many number of green marbles in the box?
Blue marble – x
xc1/27c1 = 1/3
x/27=1/3 —> x=27/3=9
No of green marbles = Total – Blue marble =27-9=18
In a bag there are 4 white, 4 red and 2 green balls. Two balls are drawn at random.What is the probability that at least one ball is of red colour?
Total Balls =10
Other than red ball = 6c2
6c2/10c2=1/3 —> 1-1/3 = 2/3
Sahil has two bags (A & B) that contain green and blue balls.In the Bag ‘A’ there are 6 green and 8 blue balls and in the Bag ‘B’ there are 6 green and 6 blue balls. One ball is drawn out from any of these two bags. What is the probability that the ball drawn is blue?
Total balls in A bag = 14, Total balls in A bag = 12
A bag = 1/2(8c1/14c1) = 2/7
B bag = 1/2(6c1/12c1) = 1/4 —> total Probability = 2/7 + 1/4 =15/28
In an examination, there are three sections namely Reasoning, Maths and English. Reasoning part contains 4 questions. There are 5 questions in maths section and 6 questions in English section. If three questions are selected randomly from the list of questions then what is the probability that all of them are from maths?
Total no of questions= 15
Probability = 5c3/15c3 = 2/91
A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that either all are green or all are red?
Total Marbles = 12
Either all are green or all are red = 5c3 + 3c3
probability = 5c3 + 3c3/12c3 = 11/220 = 1/20
A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that at least one is blue?
other than blue 8c3 / 12c3 = 14/55
probability = 1-14/55 = 41/55
A basket contains 5 red 4 blue 3 green marbles. If two marbles picked up random, What is the probability that both are red?
Probability = 5c2 / 12c2 = 5/33
A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps.If three caps are picked at random, what is the probability that two are red and one is green?
Total caps = 14
Probability = 5c2 * 2c1/ 14c3 = 5/91
A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps. If three caps are picked at random, what is the probability that none is green?
Probability = 5c0 * 9c3/ 14c3 = 3/13
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