Binomial Distribution - Maharashtra Board STD 12 Science Maths Questions

Q 1MCQ2 Marks

If the mean and variance of a binomial distribution are 5 and 2.5 respectively, then $n=$

A
5
B
10
C
18
D
15

View full solution →

Q 2MCQ2 Marks

If $X \sim B(n, P)$ and $E(X)=12, \operatorname{Var}(X)=4$, then the value of $n$ is $\ldots . .$.

A
3
B
48
C
18
D
36

View full solution →

Q 3MCQ2 Marks

The expected value of the number of heads obtained when three fair coins are tossed simultaneously is ....

A
1
B
1.5
C
0
D
-1

View full solution →

Q 4MCQ2 Marks

Given that $X \sim B (n=10, p)$. If $E ( X )=8$, then the value of $p$ is...

A
0.6
B
0.7
C
0.8
D
0.4

View full solution →

Q 5MCQ2 Marks

Given $X \sim B (n, p)$. If $p=0.6$ and $E ( X )=6$, then the value of Var. $( X )$ is......

A
2.4
B
2.6
C
2.5
D
2.3

View full solution →

Q 6Answer the following questions in short.1 Mark

If $X \sim B (n, p)$ and $n=10, E ( X )=5$, then find the value of $p$.

View full solution →

Q 7Solve the Following Question.(2 Marks)2 Marks

Given $X \sim B (n, p)$. If $E ( X )=6$, and $\operatorname{Var}( X )=4.2$, find the value of $n$.

View full solution →

Q 8Solve the Following Question.(2 Marks)2 Marks

The probability that a certain kind of component will survive a check test is 0.5 . Find the probability that exactly two of the next four components tested will survive.

View full solution →

Q 9Solve the Following Question.(2 Marks)2 Marks

If $X \sim B (n, p)$ and $E ( X )=6$ and $\operatorname{Var}( X )=4.2$, then find $n$ and $p$.

View full solution →

Q 10Solve the Following Question.(2 Marks)2 Marks

Given $X \sim B (n, p)$. If $n=10$ and $p=0.4$, find $E ( X )$ and var. (X).

View full solution →

Q 11Solve the Following Question.(2 Marks)2 Marks

The probability that a bomb will hit a target is 0.8 . Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.

View full solution →

Q 12Solve the Following Question.(3 Marks)3 Marks

If a fair coin is tossed $10$ times, find the probability of getting
$(i)$ exactly six heads.
$(ii)$ at least six heads.

View full solution →

Q 13Solve the Following Question.(3 Marks)3 Marks

Each of the total five questions in a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. The random variable $x$ is the number of questions answered correctly. What is the probability that the student will give atleast one correct answer ?

View full solution →

Q 14Solve the Following Question.(3 Marks)3 Marks

Given $X \sim B (n, p)$. If $n=20, E ( X )=10$, find $p$, Var. (X) and S.D. (X)

View full solution →

Q 15Solve the Following Question.(3 Marks)3 Marks

The probability that a person who undergoes a kidney operation will be recovered is 0.5 . Find the probability that of the 6 patients who undergo similar operations:
(a) none will recover.
(b) half of them will recover.

View full solution →

Q 16Solve the Following Question.(3 Marks)3 Marks

If a fair coin is tossed $10$ times, find the probability of getting at most six heads.

View full solution →

Q 17Solve the Following Question.(4 Marks)4 Marks

A fair coin is tossed 8 times. Find the probability that :
(i) it shows no head.
(ii) it shows head at least once.

View full solution →

Q 18Solve the Following Question.(4 Marks)4 Marks

The p.m.f. for $X =$ number of major defects in a randomly selected appliance of a certain type is

$X =x$	0	1	2	3	4
$P (x = x)$	0.08	0.15	0.45	0.27	0.05

Find the expected value and variance of $X$.

View full solution →

Binomial Distribution question types

Binomial Distribution questions

Generate a Binomial Distribution paper free

Binomial Distribution Maths - Binomial Distribution

Binomial Distribution question types

Binomial Distribution questions

Generate a Binomial Distribution paper free