1
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let A and B be two independent events such that

P(A̅) = 0.7, P(B̅) = k, P(A ∪ B) = 0.8, what is the value of k ?

A
$\frac{5}{7}$
B
$\frac{4}{7}$
C
$\frac{2}{7}$
D
$\frac{1}{7}$
2
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probability of getting tail in all the first four tosses followed by head ? 
A
$\frac{81}{512}$
B
$\frac{81}{1024}$
C
$\frac{81}{256}$
D
$\frac{27}{1024}$
3
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is probability of getting exactly three heads ?
A
$\frac{81}{256}$
B
$\frac{27}{64}$
C
$\frac{27}{256}$
D
$\frac{9}{256}$
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and p = $\frac{4}{5}$, what is the variance of Y?  
A
1
B
$\frac{1}{2}$
C
16
D
$\frac{1}{16}$
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