Sample QuestionsBinomial Distribution questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ___________
Answer: B.
View full solution →The probability of a shooter hitting a target is $\frac{3}{4}$. How many minimum numbers of times must he fie so that the probability of hitting the target at least once is more than 0.99 ?
Answer: C.
View full solution →If $X \sim B(4, p)$ and $P(X=0)=\frac{16}{81}$, then $P(X=4)=$
- A
$\frac{1}{16}$
- ✓
$\frac{1}{81}$
- C
$\frac{1}{27}$
- D
$\frac{1}{8}$
Answer: B.
View full solution →In a binomial distribution, n = 4. If 2 P(X = 3) = 3 P(X = 2) then p = ___________
- A
$\frac{4}{13}$
- B
$\frac{5}{13}$
- ✓
$\frac{9}{13}$
- D
$\frac{6}{13}$
Answer: C.
View full solution →For a binomial distribution, n = 5. If P(X = 4) = P(X = 3) then p = ___________
- A
$\frac{1}{3}$
- B
$\frac{3}{4}$
- C
$1$
- ✓
$\frac{2}{3}$
Answer: D.
View full solution →Solve the following:
Let $X ~ B(n, p).$
If $E(X) = 5$ and $Var(X) = 2.5,$ find $n$ and $p.$
View full solution →Solve the following:
Let $X \sim B(n, p).$
If $n = 10, E(X) = 5,$ find p and Var(X).
View full solution →If $E(X)=6$ and $\operatorname{Var}(X)=4 \cdot 2$, find $n$ and $p$.
View full solution →Let the p.m.f. of r.v. $X$ be
$
P(X=x)={ }^4 C_x\left(\frac{5}{9}\right)^x \times\left(\frac{4}{9}\right)^{4-x} \text {, for } x=0,1,2,3,4 .
$
then find $E(X)$ and $\operatorname{Var}(X)$.
View full solution →Given $X \sim B(n, P)$ : If $n=10, E(X)=8$, find $\operatorname{Var}(X)$.
View full solution →The probability that a certain kind of component will survive a check test is $0.6.$ Find the probability that exactly $2$ of the next $4$ tested components tested survive.
View full solution →A lot of $100$ items contain $10$ defective items. Five items are selected at random from the lot and sent to the retail store. What is the probability that the store will receive at most one defective item?
View full solution →Ten eggs are drawn successively with replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.
View full solution →Six balls are drawn successively from an urn containing 7 red and 9 black balls. Tell whether or not the trials of drawing balls are Bernoulli trials when after each draw the ball drawn is
(i) replaced
(ii) not replaced in the urn.
On a multiple-choice examination with three possible answers for each of the five questions. What is the probability that a candidate would get four or more correct answers just by guessing?
If the probability of success in a single trial is $0.01.$ How many trials are required in order to have a probability greater than $0.5$ of getting at least one success?
View full solution →The probability that a machine develops a fault within the first $3$ years of use is $0.003.$ If $40$ machines are selected at random, calculate the probability that $38$ or more will develop any faults within the first $3$ years of use.
View full solution →The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that (i) all 8 machines (ii) 7 or 8 machines (iii) at most 6 machines will produce all bolts within specification.
An examination consists of $10$ multiple choice questions, in each of which a candidate has to deduce which one of five suggested answers is correct. A completely unprepared student guesses each answer completely randomly. What is the probability that this student gets $8$ or more questions correct? Draw the appropriate moral.
View full solution →A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is $3\%.$ The inspector of the retailer picks $20$ items from a shipment. What is the probability that the store will receive at most one defective item?
View full solution →It is observed that it rains $12$ days out of $30$ days. Find the probability that
(i) it rains exactly $3$ days of the week.
(ii) it will rain at least $2$ days of a given week.
View full solution →A computer installation has 10 terminals. Independently, the probability that anyone terminal will require attention during a week is 0.1. Find the probabilities that (i) 0 (ii) 1 (iii) 2 (iv) 3 or more, terminals will require attention during the next week.
If a fair coin is tossed 10 times and the probability that it shows heads (i) 5 times (ii) in the first four tosses and tail in the last six tosses.
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
In a large school, $80\%$ of the pupil like Mathematics. A visitor to the school asks each of $4$ pupils, chosen at random, whether they like Mathematics.
(i) Calculate the probabilities of obtaining an answer yes from$ 0, 1, 2, 3, 4$ of the pupils.
(ii) Find the probability that the visitor obtains answer yes from at least$ 2$ pupils:
(a) when the number of pupils questioned remains at $4.$
(b) when the number of pupils questioned is increased to $8.$
View full solution →The probability that a mountain bike travelling along a certain track will have a tire burst is $0.05.$ Find the probability that among $17$ riders:
(i) exactly one has a burst tyre
(ii) at most three have a burst tyre
(iii) two or more have burst tyres.
View full solution →In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that (i) none (ii) 1 (iii) 2 (iv) all 3 of the sample will work.
The probability of a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one, will fuse after 150 days of use.
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that
(i) all the five cards are spades
(ii) only 3 cards are spades
(iii) none is a spade.