Probability Class Questions
Question 1: One card is drawn from a well shuffled standard pack of 52 cards. What is the probability
that is
a)
b)
c)
d)
e)
It is a king
King of red color
King of heart
Numeric card
Numeric card being multiple of 2
Question 2: A bag contains 30 balls numbered from 1 to 30 one ball is drawn at random. Find its
probability will be a multiple of
a)
b)
c)
d)
e)
f)
3
5
7
3&5
3 &7
5&7
Question 3: An unbiased cubic dice is thrown. What is the probability of getting?
a) A multiple of 3 or 5
b) A multiple of 2 or 5
Question 4: From a well shuffled pack of 52 cards one card is drawn find the probability
a)
b)
c)
d)
e)
it is either red color or black color card
it is either a heart card or diamond card
it is either a king or queen
it is either a king of red color or queen of black color
it is either a king of heart or queen of diamond.
Question 5: A bag contains 3 black, 4 white and 5 red balls. One ball is drawn at random find the
probability
a) it is either a black or non white ball
b) it is either a white ball or non-red ball
c) it is either a red ball or non-black ball
Question 6: A dice is thrown. Find the probability of
a) multiple of 2 or 3
b) multiple of 2 or 4
Question 7: five cards are drawn in succession and without replacement from an ordinary deck of 52
well shuffled cards
1)
2)
3)
4)
find probability that there no ace among the five card
find probability that their ace and least two cards are king
find probability that only first three cards are aces
find probability that an ace will appear only the fifth drawn
Question 8: P (A) =0.25, P (B) =0.15, P (AUB) =0.30 in case of dependent events find value of
a)
b)
c)
d)
e)
P(A∩B)
P(A∩B)
P(A∩B)
P(A∩B)
P(AUB)
Question 9: P (A) =0.80, P (B) =0.60, P (AUB) =0.30 in case of independent events
a)
b)
c)
d)
e)
f)
g)
h)
P(A∩B)
P(A∩B)
P(A∩B)
P(A∩B)
P(AUB)
P(A U B
P( A∩B)+ P(Ā∩B)
P(A∩B) + P(A∩B)
Question 10: what is the probability that a leap year selected at random of 55 Sundays
Question 11: A drawer contains 50 bolts and 150 nuts half of the bolts & nuts are rusted. If one item
chosen at random. What is the probability that it is rusted or it is bolt?
Question 12: for events A & B, P (AI∩ B) =0.1, P (A∩BI) =0.4 and P(AIUBI) = 0.6. Find P (A), P (B), P
(AUB), P (AIUB)
Question 13: A & B are two events P(A)=2/3, P(Ā ∩ B) =1/6, P(A∩B) =1/3 fins P(B), P(AUB),P(ĀUB) ,
P(B), P(A/B), P(B/A)
Question 14: X can solve a problem 4 out of 5, Y can solve a problem 3 out of 4, and Z can solve a
problem 2out of 5. Find the probability
a) Any two of them solve a problem
b) At least two of them solve a problem
c) Solve a problem
Question 15: A company is considering upgrading a computer system and a major portion if upgrade is
a new operating system. The company is a new operating system. The company has asked an engineer
for an evaluation of the operating system suppose the probability of favorable evaluation is 0.65. If
the probability the company will upgrade the system is given a favorable evaluation is 0.86. What is
the probability that the company will upgrade and receive a favorable evaluation?
Question 16: Among 1000 applicants for admission to MA economics course in university 600 were
economics graduate and 400 were non-economics graduate 30% of economics graduate application
and 5% of non-economics graduate applications are obtained admission. If an applicant selected at
random is found to have been given admission. What is the probability that he/she is an economics
graduate?
Question 17: Assume that a factory has two machine past records show that the machine 1 produced
30% of the item output and machine 2 produced 70% of the item output further 5% of the items
produced by machine 1 is defective and only 1% produced by machine 2 were defective. Defective
item drawn at random find probability defective item machine 1 & 2?
Question 18: A dealer in refrigerator estimate from his past experience the probability of his selling
refrigerator in a day
X:
0
1
2
3
4
5
6
Y:
0.03
0.07
0.15
0.02
0.7
0.02
0.01
Question 19: the probability that a man fishing a particular place will catch 1,2,3,4 fish are 0.4,0.3,0.2
& 0.1 respectively. What is expected number of fish caught?
Question 20: A petrol pump proprietor sells an average of Rs 80000 worth of petrol an rainy days and
on average of Rs. 95000 an clear days statistics from the meteorological department show that the
probability rainy weather on coming Monday. Find the expected value of petrol sale on coming
Monday.
Question 21: The prior probabilities for event A1 and A2 are P (A1) =0.40 and P (A2) =0.60. It is also
known that P (A1∩A2) =0. Suppose P (B/A1) =0.20 and P (B/A2) =0.05 find
a) Are A1 and A2 mutually exclusive
b) Compute (A1∩B) & (A2∩B)
c) P(B)
Question 22 : P(A1) =0.2, P(A2)=0.50, P(A3)=0.30, P(B/A1)=0.50, P(B/A2)=0.40, P(B/A3)=0.30 find
a) P(B∩A1)
b) P(B∩A2)
c ) P(B∩A3)
Question 23: A bag contains 3 black, 4 white and 5 red balls. One ball is drawn at random find the
probability
a) multiple of 3 or 5
b) multiple of 3 or
Question 24: A manufacturing firm produces unit of a product in four plants. Define event Ai a unit is
produced in plant i = 1,2,3,4 and event B a unit is defective. From the past records of the proportion of
defectiveness produced at each plant the following conditional probabilities are set
P (B/A1) =0.05
P (B/A2) =0.10
P (B/A3) =0.15
P (B/A4) =0.02
The first plant produces 30 % of the units of the product, the second plant 25 %, third plant 40 % and the
fourth plant 5 %. A unit of the product made at one of these plants and is found to be defective. What is
the probability that the unit was produced in plant 3?
Question 25: A bag contains 8 white and 4 red balls five balls are drawn at random. What is the
probability that 2 of them are red and 3 white?
BINOMIAL
Question 26: A coin is tossed six times what is the probability if obtaining four or more heads
Question 27: Assuming that it is true that 2 in 10 industrial accidents are due to fatigue, find the
probability that
a) Exactly 2 of 8 industrial accident will be fatigue
b) At least 2 of the 8 industrial accident will be fatigue
Question 28: The proportion of a male & female student in a class is found to be 1:2. What is the
probability that out of 4 students selected at random with replacement, 2 or more will be females?
Question 29:. The probability of a bomb hitting a target is 1/5. Two bombs are enough to destroy a
bridge. If six bombs are aimed at the bridge, find the probability that the bridge is destroyed.
Question 30: Insurance sell policies to 5 men all of identical age and good health. According to the
actuarial tables, the probability that a man of this particular age will be alive 30 years hence 2/3. Find
the probability those 30 years hence
I)
II)
At least 1 man will be alive
At least 3 men will be alive
Question 31: In a large group of students 80% have a recommended statistics book. Three students
are selected at random. Find the probability distribution of the number of students having the book.
Also compute the mean and variance of the distribution.
Question 32: Mean & variance of discrete random variable are 6 and 2 respectively. Assuming x to
binomial variate find (5≤ x ≤ 7)
Question 33: The probability function of a binomial distribution
Question 34: Eight coins are tossed at a time of 256 times. Number of heads observed at each throw is
recorded and the results are given below. Find the expected frequencies. What are the theoretical
value of mean & S.D? Calculate also mean and S.D of the observed frequencies
No. of heads of a throw
frequency
0
2
1
6
2
30
3
52
4
67
5
56
6
32
7
10
8
1
POISSONS DISTRIBUTION
Question 35: Average number of customer’s arrival per minute at super bazaar is2. Find the
probability that during one particular minute
a) Exactly 3 customers will arrive
b) At the most 2 customers will arrive
c) At least 1 customer will arrive
Question 36 : an executive makes an average 5 telephone calls per hour at a cost which may be taken
as Rs.2 per call determine the probability that in any hour the telephone call cost
a) Exceeds Rs.6
b) Remain Rs. Less than 10
Ques 37: Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
a. Compute the probability of receiving three calls in a 5- minute interval of time.
b. Compute the probability of receiving exactly 10 calls in 15 minute.
c. Suppose no calls are currently on hold. If the agent takes five minutes to complete the
Current calls, how many callers do you expect to be waiting by that time? What is the
Probability that none will be waiting?
d. If no calls are currently being processed, what is the probability that the agent can take three
minutes for personal time without being interrupted by a call?
Question 38 : 10% of the tools produced in a manufacturing process turn out to be defective. Find the
probability that an sample of 10 tools chosen at random. Exactly two will be defective
a) The binomial distribution
b) The poisons approximation to the binomial distribution.
Question 39: suppose an average 1 house in 1000 in a certain district has a fire during a year. if there
are 2000 houses in that district what is the probability that exactly 5 house will have a fire during the
year.
Normal Distribution
Question 40: find the area under the normal curve
Question 41: find the area to right of z=0.25
Question 42: The Mumbai municipal corporation installed 2000 bulbs in the streets of Mumbai. If
these bulbs have an average life of 1000 burning hours, with a standard deviation of 200 hours, what
number of bulbs might be expected to fail in the first 700 burning hours? The table of area of the
normal curve at selected values is as follows
Z
Probability
1.0
12.5
0.159
0.106
1.50
0.067
Question 43: In an intelligence test administered to 1000 students the average score was 42 ans
standard deviation is 24. Find
A) The number of students exceeding a score of 50
B) The number of students lying between 30 and 54
Question 44 : 1) 15000 students appeared for an examination. The mean marks were 49 and S.D. of
marks was 6. Assuming the marks to be normally distributed, what proportion of students scored
more than 55 marks?
2) if in the same examination Grade ‘A’ is to be given students scoring more than 70 marks what
proportion of the students will receive grade ‘A’