Braj Education Centre
Cultivating Academic Minds
Class XII (MATHEMATICS) ASSIGNMENT : PROBABILITY
1. A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red
balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise
bag B. If two balls are drawn at random (without replacement) from the
selected bag, find the probability of one of them being red and another black
2. An unbiased coin is tossed 4 times. Find the mean and variance of the number
of heads Obtained.
3. If
A
P (=
A ∩ B)
and
B
are
two
independent
events
such
that
2
1
and P (=
A∩ B)
, find P ( A) and P ( B )
15
6
4. Three balls are drawn one by one without replacement from a bag containing 5
white and 4 green balls. Find the probability distribution of number of green
balls drawn.
5. A fair die is rolled. lf I turns up, a ball is picked up at random from bag A, if2 or
3 turns up, a ball is picked up at random from bag B, otherwise a ball is picked
up from bag C. Bag A contains 3 red and 2 white balls, bag B contains 3 red
and 4 white balls and bag C contains 4 red and 5 white balls. The die is rolled,
a bag is picked up and a ball is drawn from it. If the ball drawn is red, what is
the probability that bag B was picked up?
6. A coin is biased so that the head is 3 times as likely to occur as tail. If the coin
is tossed three times, find the probability distribution of number of tails.
7. In an examination, 10 questions of true - false type are asked. A student
tosses a fair coin to determine his answer to each question. If the coin falls
heads, he answers ' true' and if it falls tails, he answers ' false '. Show that the
probability that he answers at most 7 questions correctly is
121
128
8. A speaks truth in 60% of cases, while B in 90% of the cases. In what percent
cases are they likely to contradict each other in stating the same fact? In the
case of contradiction, do you think, the statement of B will carry more weight
as he speaks truth in more number of cases than A?
9. P and Q speak truth in 70% and 80% cases respectively. In what percent
cases will they agree with each other, while stating the same fact? Do you
think that when they agree on a fact they are both speaking the truth?
10. The probability of simultaneous occurrence of at least one of two events A and
B is p. If the probability that exactly one of A, B occurs is q, then prove that
P ( A′) + P=
( B′)
Call me 24 x 7 @
22711085; 9818501969
1
2 – 2 p + q.
email: s_braj@rediffmail.com
Braj Education Centre
Cultivating Academic Minds
Call me 24 x 7 @
22711085; 9818501969
2
email: s_braj@rediffmail.com