Permutation and Combination (Algebra, Teaching Exam Part-3)

Total Questions: 68

61. There are 7 possibilities of winning drawing and losing in a football match. If A is chosen at random, then what is the probability that he predicts matches correctly. [TGT 2005]

Correct Answer: (b) 16/3⁷
Solution:

Chances of winning in a match= 1/3
Chances of losing in a match = 1/3
Probability of draw the match = 1/3
∵ Out of the three events, only one event will happen i.e. All three events are mutually exclusive events.
∵ All events are independent.
∵Probability

But 4 matches are being predicted by A that is, in 1 match only 1 result will be obtained out of 3 situation, so in 1 match we will obtain 2 wrong and 1 correct result. similarly, in 4 matches = 16
Therefore, the probability that A has predicted matches is correct = 16/3⁷

62. If the probabilities of A and B being a live at the end of the year are pand q respectively, then what is the probability that one of then will be alive at the end of the year. [TGT 2005]

Correct Answer: (c) q+p-pq
Solution:

Probability of A will die within a year = p
Probability of A does not survive =1-p
Probability of B will die within a year = q
∴ If the probability of A's death is p then the probability of A's life is (1-p) and
Probability that neither of then survive =(1-P) (1-q)
= (1-p-q+pq)
∴ Probability that one of the two does not survive
= 1-(1-p-q+pq) = p+q-pq

63. How many triangles can be formed from the angular point of an octagon is not equal to the side of the triangle? [TGT 2005]

Correct Answer: (d) None of these
Solution:

64. The probabilities of three mutually exclusive events A, B and C are 2/3, 1/4 and 1/6 respectively then statement: [TGT 2005]

Correct Answer: (b) is false
Solution:

65. A cubical dice is tossed 6 times. What is the probability that 2 and 4 will come up three times each? [TGT 2005]

Correct Answer: (b) 1/46656
Solution:

66. In an experiment, a coin is tossed three times in which heads are obtained twice. If the same test is repeated three times, what will be the probability of not getting success? [TGT 2005]

Correct Answer: (c) (5/8)³
Solution:

67. If four whole numbers taken at random are multiplied together, then the chance that the last digit in the product is 1, 3, 7 or 9 is [TGT 2004]

Correct Answer: (b) 16/625
Solution:

68. Solve the following equation? [TGT 2004]

Correct Answer: (a)
Solution: