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A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both hearts. Find the Probability of the lost card being a heart?
Total cards = 52
Drawn cards(Heart) = 2
Present total cards = total cardsdrawn cards =522=50
Remaining Card 132 = 11
Probability = 11/50
There are three boxes each containing 3 Pink and 5 Yellow balls and also there are 2 boxes each containing 4 Pink and 2 Yellow balls. A Yellow ball is selected at random. Find the probability that Yellow ball is from a box of the first group?
A fruit basket contains 10 Guavas and 20 Bananas out of which 3 Guavas and 5 Bananas are defective. If two fruits selected at random, what is the probability that either both are Bananas or both are nondefective?
P(A) = 20c2 / 30c2, P(B) = 22c2 / 30c2
P(A∩B) = 15c2 / 30c2
P(A∪B) = P(A) + P(B) – P(A∩B) ⇒ (20c2/30c2)+(22c2/30c2) (15c2/30c2)=316/435
A committee of five persons is to be chosen from a group of 10 people. The probability that a certain married couple will either serve together or not at all is?
Five persons is to be chosen from a group of 10 people = 10C5 = 252
Couple Serve together = 8C3 * 2C2 = 56
Couple does not serve = 8C5 = 56
Probability = 102/252 = 51/126
Out of 13 applicants for a job there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is
Three Bananas and three oranges are kept in a box. If two fruits are chosen at random, Find the probability that one is Banana and another one is orange?
Total probability = 6C2 = 15
Probability that one is Banana and another one is orange = 3C1 * 3C1 = 9
probability = 9/15 = 3/5
A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If three balls picked up random, What is the probability that all three are White?
Total Balls = 15
Probability = 6c3 / 15c3 = 4/91
A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If three balls are picked at random, what is the probability that two are Black and one is Green?
Total Balls = 15
Probability = 4c2 * 3c1/ 15c3 = 18/455
A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four balls are picked at random, what is the probability that atleast one is Black?
Total Balls = 15
Probability = 11c4/15c4 = 22/91
One is black = 1 – 22/91 = 69/91
A basket contains three blue and four red balls. If three balls are drawn at random from the basket, what is the probability that all the three balls are either blue or red?
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 =279=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 → 11/3 = 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?
Total Marbles = 12
other than blue 8c3 / 12c3 = 14/55
probability = 114/55 = 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?
Total Marbles = 12
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 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps. If four caps are picked at random, what is the probability that two are red, one is blue and one is green?
Total caps = 14
Probability = 5c2 * 4c1 * 2c1 / 14c4 = 80/1001
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?
Total caps = 14
Probability = 5c0 * 9c3/ 14c3 = 3/13
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