DEPARTMENT OF APPLIED STATISTICS & DATA ANALYTICS
F.Y.B.Sc. USMAAS102
PROBABILITY AND PROBABILITY DISTRIBUTION
Practical No.:1. Date: / / 2022
1. A box of fuses contains 20 fuses, of which 5 are defective. If 3 of the
fuses are selected at random and removed from the box in succession
without replacement, what is the probability that all 3 fuses are
defective?
2. In a large metropolitan area, the probabilities are 0.35, 0.85, and
0.29, respectively, that a family (randomly chosen for a sample survey)
owns an android television set, a HDTV set, or both kinds of sets.
What is the probability that a family owns either or both kinds of sets?
3. The completion of a construction job may be delayed because of a
strike. The probabilities are 0.60 that there will be a strike, 0.85 that
the construction job will be completed on time if there is no strike,
and 0.35 that the construction job will be completed on time if there is
a strike. What is the probability that the construction job will be
completed on time?
4. If a person visits his dentist, suppose that the probability that he will
have his teeth cleaned is 0.44, the probability that he will have a cavity
filled is 0.24, the probability that he will have a tooth extracted is 0.21,
the probability that he will have his teeth cleaned and a cavity filled is
0.08, the probability that he will have his teeth cleaned and a tooth
extracted is 0.11, the probability that he will have a cavity filled and a
tooth extracted 0.07, and the probability that he will have his teeth
cleaned, a cavity filled, and a tooth extracted is 0.03. What is the
probability that a person visiting his dentist will have at least one of
these things done to him?
5. A coin is tossed three times and the eight possible outcomes, HHH,
HHT, HTH, THH, HTT, THT, TTH, and TTT, are assumed to be equally
likely. If A is the event that a head occurs on each of the first two tosses,
B is the event that a tail occurs on the third toss, and C is the event
that exactly two tails occur in the three tosses,
(a) Are the events A and B are independent?
(b) Are the events B and C are dependent?
(c) Are the events pairwise independent?
6. In a bridge hand, west has no ace. What is the probability that his
partner has (i) no ace, (ii) 2 or more aces.
7. Cards are dealt one by one from a pack of 52 cards until an ace appears.
Show that the probability that exactly n cards are before the first ace
(51 − n)(50 − n)( 49 − n)
appears is .
13 * 51 * 50 * 49
F.Y.B.Sc. USMAAS102
PROBABILITY AND PROBABILITY DISTRIBUTION
Practical No.:1. Date: / / 2022
1. A box of fuses contains 20 fuses, of which 5 are defective. If 3 of the
fuses are selected at random and removed from the box in succession
without replacement, what is the probability that all 3 fuses are
defective?
2. In a large metropolitan area, the probabilities are 0.35, 0.85, and
0.29, respectively, that a family (randomly chosen for a sample survey)
owns an android television set, a HDTV set, or both kinds of sets.
What is the probability that a family owns either or both kinds of sets?
3. The completion of a construction job may be delayed because of a
strike. The probabilities are 0.60 that there will be a strike, 0.85 that
the construction job will be completed on time if there is no strike,
and 0.35 that the construction job will be completed on time if there is
a strike. What is the probability that the construction job will be
completed on time?
4. If a person visits his dentist, suppose that the probability that he will
have his teeth cleaned is 0.44, the probability that he will have a cavity
filled is 0.24, the probability that he will have a tooth extracted is 0.21,
the probability that he will have his teeth cleaned and a cavity filled is
0.08, the probability that he will have his teeth cleaned and a tooth
extracted is 0.11, the probability that he will have a cavity filled and a
tooth extracted 0.07, and the probability that he will have his teeth
cleaned, a cavity filled, and a tooth extracted is 0.03. What is the
probability that a person visiting his dentist will have at least one of
these things done to him?
5. A coin is tossed three times and the eight possible outcomes, HHH,
HHT, HTH, THH, HTT, THT, TTH, and TTT, are assumed to be equally
likely. If A is the event that a head occurs on each of the first two tosses,
B is the event that a tail occurs on the third toss, and C is the event
that exactly two tails occur in the three tosses,
(a) Are the events A and B are independent?
(b) Are the events B and C are dependent?
(c) Are the events pairwise independent?
6. In a bridge hand, west has no ace. What is the probability that his
partner has (i) no ace, (ii) 2 or more aces.
7. Cards are dealt one by one from a pack of 52 cards until an ace appears.
Show that the probability that exactly n cards are before the first ace
(51 − n)(50 − n)( 49 − n)
appears is .
13 * 51 * 50 * 49
