Statistics And Probability Question 28
Question: 6 coins are tossed together 64 times, if throwing a hand is considered as a success then the ex-pected frequency of at least 3 successes is
Options:
A) 64
B) 21
C) 32
D) 42
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] Here $ P=\frac{1}{2}.q=1-p=1-\frac{1}{2}=\frac{1}{2} $ n=6, N=64. Then $ P(r){{=}^{n}}C_{r}p^{r}{q^{n-1}}{{=}^{6}}C_{r}{{( \frac{1}{2} )}^{r}}.{{( \frac{1}{2} )}^{6-r}}{{=}^{6}}C_{r}{{( \frac{1}{2} )}^{6}} $
$ \therefore f(r)=Np(r)={{64.}^{6}}C_{r}.\frac{1}{64}{{=}^{6}}C_{r} $ Now $ \sum\limits_3^{6}{p(r)=p(3)+p(4)+p(5)+p(6)} $ $ ={{(}^{6}}C_3{{+}^{6}}C_4{{+}^{6}}C_6)\frac{1}{2^{6}} $ $ =(2^{6}{{-}^{6}}C_0{{-}^{6}}C_1{{-}^{6}}C_2)\frac{1}{2^{6}} $ $ =(64-1-6-15)\frac{1}{2^{6}}=\frac{42}{64}=\frac{21}{32} $
$ \therefore ,f(r){,_{r\ge 3}}=N\sum\limits_3^{6}{p(r)=64.}\frac{21}{32}=42 $
BETA
