Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is_________?

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Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is_________?

A. 10/17
B. 10/19
C. 46/105
D. Cannot be determined
Explanation:
There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.

A 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?

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A 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. 4/9
B. 5/9
C. 7/9
D. 8/9
Explanation:
Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9

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?

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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. 3/22
B. 4/21
C. 2/21
D. 1/14
Explanation:
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) = 2/21

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?

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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. 1/455
B. 2/455
C. 1/91
D. 4/455
Explanation:
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 four marbles are picked at random, what is the probability that none is blue?

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A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?

A. 17/91
B. 33/91
C. 51/91
D. 65/91
Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91

A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.

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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 all the four bulbs are defective.

A. 62/63
B. 125/126
C. 1/63
D. 1/126
Explanation:
Out of nine, five are good and four are defective. Required probability = ⁴C₄/⁹C₄ = 1/126

Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is__________?

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Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is__________?

A. 7/12
B. 5/9
C. 1/36
D. 5/12
Explanation:
No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.

Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -.

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Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -.

A. 1/216
B. 1/36
C. 5/9
D. 5/12
Explanation:
It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36