Page 196 - Engineering Mathematics Workbook_Final

Probability & Statistics

196. In class of 200 students, 125 students 199. The box 1 contains chips numbered 3,
have taken programming language 6, 9, 12 and 15. The box 2 contains
course, 85 students have taken data chips numbered 11, 6, 16, 21 and 26.
structures course, 65 students have Two chips, one from each box are
taken computer organization course, drawn at random.
50 students have taken both The number written on these chips
programming languages and data are multiplied. The probability for the
structures, 35 students have taken product to be an even number is
both programming languages and _____
computer organization, 30 students 6 2
have taken both data structures and (a) 25 (b)
5
computer organization, 15 students
have taken all the three courses. How 3 19
many students have not taken any of (c) (d)
the three courses? 5 25
(a) 15 (b) 20 [GATE 2009 (IN)]
200. A and B friends. They decide to meet
(c) 25 (d) 35 between 1PM and 2 PM on a given
[GATE-2004 (IT)] day. There is a condition that
197. A bag contains 10 blue marbles, 20 whoever arrives first will not wait for
black marbles and 30 red marbles. A the other for more than 15 minutes.
marble is drawn from the bag, its The probability that they will met on
colour recorded and it is put back in that day is
the bag. This process is repeated 3 (a) 1 (b) 1
times. The probability that no two of 4 16
the marbles drawn have the same
colour is 7 9
1 1 (c) (d)
(a) (b) 16 16
36 6 201. Assume for simplicity that N people,
all born in April (a month of 30
1 1 days), are collected in a room.
(c) (d)
4 3 Consider the event of at least two
[GATE-2005 (IT)] people in the room being born on the
198. In a game, two players X and Y are same date of the month, even if in
tossing a coin alternately. Whoever different year, e.g. 1980 and 1985.
gets a ‘head’ first, wins the game and What is the smallest N so that the
the game is terminated. Find the probability of this event exceeds 0.5?
chance that player X will win the (a) 20 (b) 7
game if he starts?
(a) 1/3 (b) 1/2 (c) 15 (d) 16
[GATE-2009-EE]
(c) 2/3 (d) 3/4

194