Page 202 - Engineering Mathematics Workbook_Final

Probability & Statistics

239. A person decides to toss a fair coin at the end of 11 steps he is one step
repeatedly until he gets a head. He away from the starting point is
will make at most 3 tosses. Let the
random variable Y denote the number (a)   6   5 (b) 462   6   5
of heads. The value of var(Y). where   25       25    

var(.) denotes tie variance, equals:
  1   5   1   5
7 49 (c) 538     (d)    
(a) (b)  25   25 
8 64
7 105 [JNU]
(c) (d)
64 64 243. In a manufacturing plant, the
probability of making a defective bolt
[GATE 2017 EE SESSION-II] is 0.1. The mean and standard
deviation of defective bolts in a total
BINOMIAL DISTRIBUTION
of 900 bolts are respectively

240. The probability of India winning a (a) 90 and 9 (b) 9 and 90
test match against England is 0.5.
Assuming independence of the result (c) 81 and 9 (d) 9 and 81
of various matches the chance that in [GATE, EE: 2000]
a 5 match series. India’s second win
rd
occurs at 3 test is ____. 244. An unbiassed coin is tossed an
infinite number of times. The
241. A die hastbur blank faces and two probability that the fourth head
faces marked 3. The chance of getting appears at the tent toss is
a total of 12 in 5 the is (a) 0.067 (b) 0.073

    (c) 0.082 (d) 0.091
4
1
2
5
(a) C    
  
    
3
3
    [GATE-2014-EC-SET 3]
    4 245. The probability that a screw
2
1
   
5
(b) C 4      manufactured by a company is
  
3
3
   
defective is 0.1. The company sells
 1  5 screws in packets containing 5 screws
5
(c) C 4       and gives a guarantee of replacement
 6  if one or more screws in the packet
(d) None of these are found to be defective. The
probability that a packet would have
242. A man takes a step forward with to be replaced is ____.
probability 0.4 and ackward with
probability 0.6. The probability that [GATE 2016-ME-SET 2]

200