DEPARTMENT OF APPLIED STATISTICS & DATA ANALYTICS
F.Y.B.Sc. USMAAS102
PROBABILITY AND PROBABILITY DISTRIBUTION
Practical No.:2. Date: / /2022
1. A person appears for 4 tests in succession. The probability of his
passing each succeeding test is p or p/2 according as he passes or
fails the preceding test. He qualifies provided he passes at least 3
tests. What is his chance of qualifying?
2. The probability that a new film will get an award for its story is 0.23,
the probability that it will get an award for its music is 0.15 while the
probability that it gets an award for both is 0.07. What is the
probability that the film will get an award for (i) at least one of the
two?; (ii) exactly one of the two.
3. Box A contains 6 white and 4 black balls. Box B contains 5 white and
3 black balls.
(i) One ball is transferred from A to B and then a ball is drawn from
B. What is the probability that it is white?
(ii) One of the two boxes is selected at random and a ball is drawn
from it. What is the probability that it is white?
4. Three urns contain respectively 1 white - 2 black, 3 white- 1 black, &
2 white-3 black balls in each urn. A ball is drawn from each urn.
What is the probability that among the balls drawn there are exactly
2 white & 1 black ball?
5. An urn contains 10 balls of which three are black and seven are red.
The following game is played. At each trial, a ball is selected at
random, its colour is noted and it is replaced in the urn along with
two additional balls of the same colour. In three successive trials,
find the probability of selecting a black ball, in each of the three
trials.
6. An urn contains five red and three white balls. A ball is selected at
random, discarded and two balls of the opposite colour are placed in
the urn. A second ball is then selected at random from the urn, what
is the probability that both the balls have the same colour?
F.Y.B.Sc. USMAAS102
PROBABILITY AND PROBABILITY DISTRIBUTION
Practical No.:2. Date: / /2022
1. A person appears for 4 tests in succession. The probability of his
passing each succeeding test is p or p/2 according as he passes or
fails the preceding test. He qualifies provided he passes at least 3
tests. What is his chance of qualifying?
2. The probability that a new film will get an award for its story is 0.23,
the probability that it will get an award for its music is 0.15 while the
probability that it gets an award for both is 0.07. What is the
probability that the film will get an award for (i) at least one of the
two?; (ii) exactly one of the two.
3. Box A contains 6 white and 4 black balls. Box B contains 5 white and
3 black balls.
(i) One ball is transferred from A to B and then a ball is drawn from
B. What is the probability that it is white?
(ii) One of the two boxes is selected at random and a ball is drawn
from it. What is the probability that it is white?
4. Three urns contain respectively 1 white - 2 black, 3 white- 1 black, &
2 white-3 black balls in each urn. A ball is drawn from each urn.
What is the probability that among the balls drawn there are exactly
2 white & 1 black ball?
5. An urn contains 10 balls of which three are black and seven are red.
The following game is played. At each trial, a ball is selected at
random, its colour is noted and it is replaced in the urn along with
two additional balls of the same colour. In three successive trials,
find the probability of selecting a black ball, in each of the three
trials.
6. An urn contains five red and three white balls. A ball is selected at
random, discarded and two balls of the opposite colour are placed in
the urn. A second ball is then selected at random from the urn, what
is the probability that both the balls have the same colour?
