Page 195 - Engineering Mathematics Workbook_Final

Probability & Statistics

190. Two busses A and B are scheduled to 27 18
arrive at a town central bus station at (c) 75 (d) 25
noon. The probability that bus A will 193. A box contains 5 black balls and 3
be late is 1/5. The probability that bus red balls. A total of three balls are
B will be late is 7/25. The probability picked from the box one after

that the bus B is late given that bus A another, without replacing them back.
is late is 9/10. Then, The probability of getting two black
balls and one red ball is
3
(a) probability that neither bus will be (a) (b) 2
late on a particular day is 7/10 8 15

(b) probability that bus A is late given 15 1
that bus B is late is 18/28 (c) 28 (d)
2
[GATE-1997]
(c) probability that at least one bus is 194. Seven car accidents occurred in a
late is 3/10 week, what is the probability that

(d) probability that at least one bus is they all occurred on the same day?
in time is 4/5 (a) 1 (b) 1
7 7 7 6
191. The chance of a student passing an

exam is 20%. The chance of a student (c) 1 (d) 2
passing the exam and getting above 2 7 2 7
90% in it is 5%. Given that a student [GATE-2001]
passes the examination, the
probability that the student gets above 195. Manish has to travel from A to D
90% marks is changing buses at stops B and C
enroute. The maximum waiting time

1 1 at either stop can be 8 minutes each,
(a) (b) but any time of waiting up to 8
18 4 minutes is equally likely at both

places. He can afford up to 13
2 5
(c) (d) minutes of total waiting time if he is
9 18 to arrive at D on time. What is the
probability that Manish will arrive
[GATE 1992] late at D?
192. The probability that a number 8 13
selected at random between 100 and (a) (b)
999 (both inclusive) will not contain 13 64
the digit 7 is 119 9

16  9  3 (c) (d)
(a) (b)       128 128
25  10  [GATE-2002-ME]

193