# Math for Computer science Questions and Answers 71 to 80

## Math for Computer science

### Questions 71 to 80

71.
If P(A’) = 3/8, P(B’) =1/2 and P(A∩ B) = 1 / 4, then P(A/B) = -----------.
(a)                           1/2                          (b) 1/8                     (c) 1 / 4                   (d) 2/5  (e) 2/8.

72.
Suppose a coin is flipped three times. Let X(t) be the random variable that equals the number of tails that appears and t is the outcome, then X(HTT) = _____.
(a) 3                        (b) 2                        (c) 1                        (d) 0                        (e) 4.

73.
A coin is tossed and a single 6-sided die is rolled. What is the probability of landing on the head side of the coin and rolling a 3 on the die?
(a) ½                       (b) 1/12                   (c) 1/3                     (d) 1/6                     (e) 2/3.

74.
How many functions are there from a set with m elements to one with n elements?
(a) nm                     (b) nm+1                                       (c) mn                                            (d) mn+1                                       (e) m + n.

75.
The values of n and r, if P(n,r) = 7920, are
(a)                           10 , 3                      (b) 12, 4                  (c) 11, 4                  (d) 10 , 4                              (e) 11, 8.

76.
An integer s is an inverse of a modulo m if
(a)                           a ≡ s (mod m)                                        (b) s ≡ a (mod m)
(c)                           s.a ≡ 1 (mod m)                                     (d) m.s ≡ 1 (mod a)
(e)                           m.a ≡ 1 (mod s).

77.
A drawer contains a dozen brown socks and a dozen black socks, all unmatched. A man takes out socks at random in the dark. How many socks must he take to be sure that he has at least two socks of the same color?
(a)                           3                             (b) 13                      (c) 14                      (d) 12   (e) 2.

78.
A finite state machine with output, where the output is determined only by the state, is
(a)                           Kleene machine                                     (b) Mealy machine
(c)                           Moore machine                                      (d) Deterministic Finite state automata.
(e)                           Non-deterministic Finite state automata.

79.
The grammar which has no restrictions on its productions is
(a)                           Type 0 Grammar                                    (b) Type 1 Grammar
(c)                           Type 2 Grammar                                    (d) Type 3 Grammar             (e) Type 4 Grammar.
80.
Let A = {F, {F}} then which of the following statement is true?
 (a) F Î F (b) Fc Í A (c) {F} Î P(A) (d) A Î F (e) A Í {F}.

#### Answers

 71. Answer :      (a) Reason : The student can select the three projects from three lists one after the other in 23+15+19 = 57 ways (Sum rule). 72. Answer :      (a) Reason : P(A/B) = P(A∩B) / P(B) = (1/4) / (1–1/2) = 1/2 73. Answer :      (b) Reason : A random variable is a function from the sample space of an experiment to the set of real numbers. 74. Answer :      (a) Reason : A function corresponds to a choice of one of the n elements in the codomain for each of the m elements in the domain. Henc tby the product rule there are n.×n×….×n = nm functions from a set with m elements to one with n elements. 75. Answer :      (c) Reason : P(n,r) = 7920;   7920 = 792 * 10 = 11*10*72 = 11*10*9*8 = P(11, 4)           Therefore , n= 11,r = 4. 76. Answer :      (c) Reason : no explanation. 77. Answer :      (b) Reason : Let us suppose the man picks black sock first and then brown sock. In the 3rd attempt he has to either pick black or brown so he is having two socks of same color. So according to pigeon hole principle he has to pick a minimum number of three socks to have at least two socks of the same color. pigeon hole principle explains worst case scenario. 78. Answer :      (c) Reason : The finite state machine with output, where the output is determined only by the state is Moore machine. 79. Answer :      (a) Reason : The grammar which has no restrictions on its productions is Type 0 Grammar 80. Answer :      (c) Reason:  By definition of power set of a set.

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