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A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue ?
A. 4/455
B. 34
C. 2/455
D. 1/455Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow ?
A. 1/14
B. 2/21
C. 3/22
D. 4/21Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color ?
A. 5/9
B. 8/9
C. 6
D. 7/9Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is ______ ?
A. 10/19
B. 46/105
C. 10/17
D. Cannot be determinedWhat is the probability that a leap year has 53 Sundays and 52 Mondays ?
A. 2/7
B. 5/7
C. 1/7
D. 010 books are placed at random in a shelf. The probability that a pair of books will always be together is _____ ?
A. 1/5
B. 3/10
C. 1/10
D. 9/10Probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on at least one ticket is ______ ?
A. 0.6234
B. 0.5834
C. 0.5904
D. 0.4869In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?
A. 9/14
B. 16/21
C. 5/21
D. 5/14Probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact ?
A. 17/35
B. 19/35
C. 18/35
D. 12/35Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them ?
A. 5/6
B. 3/8
C. 1/6
D. 5/8