Probability

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. 6/63
B. 2/63
C. 125/126
D. 1/126
Explanation:
Required probability = 1 – 1/126 = 125/126

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

A. 5/9
B. 5/12
C. 1/36
D. 7/12
Explanation:
Using question number 11 and 12, we get the probability as
1 – (1/36 + 5/9) = 5/12

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.

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. 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. 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

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

A. 19/52
B. 17/52
C. 5/13
D. 4/13
Explanation:
P(SᴜK) = P(S) + P(K) – P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 – 1/52 = 4/13