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

Total Questions: 68

51. For any two independent events E₁, and E₂, P{(E₁,)∪(E₂)∩(E̅₁)∩(E̅₂)} is [TGT 2010]

Correct Answer: (d)
Solution:

52. Solve the following equation? [TGT 2009]

Correct Answer: (c)
Solution:

53. If A and B are arbitrary events then: [TGT 2009]

Correct Answer: (b) P(A∪B) ≥ P(A) + P(B) -1
Solution:

If event A and event B are arbitrary events. Then P(A∪B) ≥ P(A) + P(B) -1

54. If P(A) = 0.65, P(B) = 0.15, then P(A̅)+P(B̅) will be- [TGT 2009]

Correct Answer: (a) 1.2
Solution:

Given, P(A) = 0.65, P(B) = 0.15,
Then, P(A̅)+P(B̅)=(1-P(A)) + (1–P(B))
= (1-0.65)+(1–0.15) = 2-.80 = 1.2

55. How many words can be grouped with the word "LEADER"? [TGT 2009]

Correct Answer: (c) 360
Solution:

56. 2 Cards are drawn at random from a new deck of 52 cards, then what is the probability that one of the cards is a spade and the other is an ace? [TGT 2009]

Correct Answer: (b) 8/221
Solution:

57. If total 7 trains are available for departure and 7 trains for arrival from Kanpur to Jhansi. Then tell a person who wants to come from Jhansi to Kanpur, in how many ways can be come and go, while he does not use the train by which he comes? [TGT 2009]

Correct Answer: (b) 42
Solution:

58. A bag contains 3 black and 4 white balls. Two balls are drawn one after the other at random with replacement, threw what is the probability that the ball drown the second time is white?

Correct Answer: (c) 4/7
Solution:

Total number of balls = 4+3=7
∴ Events are independent. Because if one ball comes out black, it is not necessary that it will not come out black next time.
Probability of drawing a black ball for the first time

Probability of drawing white ball for the second time

{∴One ball is out.
∴ combined probability of getting both =

Similarly, if the white ball is drawn for the first time, then the probability

And, for the second time also the white ball comes out, then it's probability

Hence, Joint probability

∵ Both the above events are mutually exclusive events, because if the first event happens then the second will not happen and if the second happens then the first will not happen.
Therefore, the probability of getting the white ball for the second time is

59. Out of 13 cricket players, four are bowlers. How many ways a group of 11 players can be formed in which there must be at least 2 bowlers? [TGT 2009]

Correct Answer: (c) 78
Solution:

∴Total number of players = 13
∴ Out of 11, taking 2 bowlers, number of other players = 9
∴ Total number of ways to form the group = ⁴C₂. ⁹C₉ 6×1 = 6
Taking 3 bowlers out of 11 goes to 8 other players.
Total method = ⁴C₃.⁹C₈= 4×9 = 36
Similarly, Taking 4 bowlers out of 11 goes to 7 other players.
Total method = ⁴C₄. ⁹C₇ = 1×(72/2) = 36
So, total ways of playing 11 players together and having at least 2 bowlers = 6+36+36 = 78

60. There are 10 mangoes in a bag out of which 4 are rotten. If 2 mangoes are taken out from the bag together what is the probability that both are good (not rotten). [TGT 2005]

Correct Answer: (d) None of these
Solution:

Methods of taking out of 2 mangoes from a total of 10 manages = ¹⁰C₂
The probability of taking out 2 mangoes from 4 mangoes (not rotten)
Therefore, the probability of getting 2 mangoes which are rotten that is they are not good
Probability of rotten mangoes =