Page 188 - Engineering Mathematics Workbook_Final

Probability & Statistics

Binomial Distribution 1 7
(a) 5 (b)
148. The probability of getting a total of 7 5 15
at least once in three tosses of a pair 25 8!     3
7
1
5
of fir dice is (c) (d)    
    
  
36 3!5! 6 6
   
125 91
(a) (b) 152. Out of 2000 families with 4 children
216 216
each. How many families would you
117 99 expect to have atleast one boy?
(c) (d)
216 216
(a) 1250 (b) 1875
149. The mean and variance of number of (c) 1500 (d) 1825
heads resulting from 10 independent
tosses of a fair coin respectively, are Poission Distribution

5 153. The second moment of a poisson –
(a) 5, (b) 10, 5
2 distributed random variable is 2. The
mean of the random variable is
5 5 1 1
(c) , (d) , 154. An observer counts 240 veh/h at
2 4 2 4
specific highway location. Assume

150. Consider an unbiased cubic die with that the vehicle arrival at the location
opposite faces coloured identically is poisson distributed. Find the
and each face coloured red, blue or probability of having
green such that each colour appears
only two times on the die. If the die is (i) One vehicle arriving over a 30
thrown thrice, the probability of second time interval.
obtaining red colour on the top face (ii) Atleast one vehicle arriving over
of the die atleast twice is ______ a 30 second time interval.

151. An archer makes 10 independent (iii) More than 2 vehicles arriving
attempts at a target and his over a 30 second time interval.
probability of hitting the target at
5 155. Let X be a binomial random variable
each attempt is . Then the 3
6 with n = 10 and P = and Y be
conditional probability that his last 4
two attempts are successful given that poission random variable with mean
he has a total of 7 successful attempts  = 2. If X, Y are independent, then

is P ( XY = ) 0 is

186