Page 165 - Engineering Mathematics Workbook_Final

Probability & Statistics

1. Suppose A and B are two 4. Two players, A and B, alternately
independent events with probabilities keep rolling a fair dice. The person to
P A  P B  get a six first wins the game. Given
( ) 0 and ( ) 0 . Let A and
that player A starts the game, the
B be their complements. Which one probability that A wins the game is
of the following statements is
FALSE? 5 1
(a) 11 (b) 2

P
(a) ( A B = ) P A P B
( ) ( )
7 6
)
P
(b) ( | A B = P ( ) A (c) 13 (d) 11
)

P
( )
(c) ( A B = P ( ) A + P B [GATE-2015-EE-SET-1]
( ) ( )
(
)

(d) P A B = P A  P B 5. Ram and Ramesh appeared in an
interview for two vacancies in the
same department. The probabilities of
[GATE-2015-EC-SET-1]
Ram’s selection is 1/6 and that of
2. Three vendors were asked to supply a Ramesh is 1/8. What is probability
very high precision component. The that only one of them will be

respective probabilities of their selected.
meeting the strict design (a) 47/48 (b) 1/4
specifications are 0.8, 0.7 and 0.5.
Each vendor supplies one component. (c) 13/48 (d) 35/48
The probability that out of total three
components supplied by the vendors [GATE-2015-EC-SET-2; ME - SET-1]
at least one will meet the design 6. Two coins R and S are tossed. The 4

specifications is __________. joint events H H , T T , T H
S
R S
R
S
R
[GATE-2015] have probabilities 0.28, 0.18, 0.30,
0.24 respectively, where H represents
3. If P(X) = 1/4, P(Y) = 1/3 and head and T represents tail. Which one
P ( X  Y ) 1/12= , the value of of the following is TRUE?
P(Y/X) is
(a) The coin tosses are independent

1 4
(a) (b) (b) R is fair, S is not
4 25
(c) S is fair, R is not
1 29
(c) (d) (d) The coin tosses are dependent
3 50

[GATE-2015-EE-SET-2]
[GATE-2015-ME-SET-3; 1 MARK]

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