Probability Question 101
Question: A die is tossed thrice. A success is getting 1 or 6 on a toss. The mean and the variance of number of successes
[AI CBSE 1985]
Options:
A) $ \mu =1,{{\sigma }^{2}}=2/3 $
B) $ \mu =2/3,{{\sigma }^{2}}=1 $
C) $ \mu =2,{{\sigma }^{2}}=2/3 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
For binomial distribution, mean $ =np $ and variance $ =npq $
$ n=3, $
$ p=\frac{2}{6}=\frac{1}{3}, $
$ q=1-p=1-\frac{1}{3}=\frac{2}{3} $ So, mean $ (\mu )=3\times \frac{1}{3}=1 $ Variance $ ({{\sigma }^{2}})=3\times \frac{1}{3}\times \frac{2}{3}=\frac{2}{3} $ .
BETA
