Probability

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

A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is__________?

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A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is__________?

A. 25/42
B. 9/20
C. 10/23
D. 41/42
Explanation:
Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42.

A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.

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A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.

A. 8/15
B. 2/5
C. 3/5
D. 7/15
Explanation:
Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 7/15

If six persons sit in a row, then the probability that three particular persons are always together is____________?

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If six persons sit in a row, then the probability that three particular persons are always together is____________?

A. 1/20
B. 3/10
C. 1/5
D. 4/5
Explanation:
Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5