A bag contains 6 red balls 11 yellow balls and 5 pink balls. If two balls are drawn at random from the bag. One after another what is the probability that the first ball is red and second ball is yellow?
Clearly, there are 52 cards, out of which there are 12 face cards.
Probability of getting a face card = 12/52 = 3/13
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Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35
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The probability that Soumya will get marry within 365 days is ‘a’ and the probability that her colleague Alma get marry within 365 days is ‘b’. Find the probability that only one of the two gets marry at the end of 365 days.
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
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There are 8 boys and 12 girls in a class. 5 students have to be chosen for an educational trip. Find the number of ways in which this can be done if 2 particular girls are always included.
There are 7 red balls and 8 yellow balls in a bag. Two balls are simultaneously drawn at random. What is the probability that both the balls are of same colour ?
Total balls in the bag = 7 + 8 = 15
Total possible outcomes = Selection of 2 balls out of 15 balls
= 15C2 = (15*14) / (1*2) = 105
Total favourable outcomes = Selection of 2 balls out of 8 yellow balls + Selection of 2 balls out of 7 red balls
= 8C2 + 7C2 = [(8*7)/(1*2)] + [(7*6)/(1*2)]
= 28 + 21 = 49
Required probability = 49/105 = 7/15
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There are four hotels in a town. If 3 men check into the hotels in a day then what is the probability that each checks into a different hotel?
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -.
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
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A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
In a race where 12 cars are running, the chance that car X will win is 1/6, that will win is 1/10 and that Z will win is 1/8. Assuming that a dead heat is impossible. Find the chance that one of them will win.
A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:
Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅
= (10 x 6)/252 = 5/21
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There are 10 Letters and 10 correspondingly 10 different Address. If the letter are put into envelope randomly, then find the Probability that Exactly 9 letters will at the Correct Address ?
As we know we have 10 letter and 10 different address and one more information given that exactly 9 letter will at the correct address….so the remaining one letter automatically reach to their correct address
P(E) = favorable outcomes /total outcomes
Here favorable outcomes are ‘0’.
So probability is ‘0’.
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Two dice are tossed. The probability that the total score is a prime number is:
