A) \[\frac{119}{128}\]
B) \[\frac{119}{228}\]
C) \[\frac{19}{128}\]
D) \[\frac{18}{128}\]
Correct Answer: A
Solution :
[a] We have, \[P(\left| X-4 \right|\le 2)=P(-2\le X-4\le 2)=P(2\le X\le 6)\] \[=1-[P(X=0)+P(X=1)+P(X=7)+P(X=8)]\] \[=1-\left[ ^{8}{{C}_{0}}{{\left( \frac{1}{2} \right)}^{8}}{{+}^{8}}{{C}_{1}}{{\left( \frac{1}{2} \right)}^{8}}{{+}^{8}}{{C}_{7}}{{\left( \frac{1}{2} \right)}^{8}}{{+}^{8}}{{C}_{8}}{{\left( \frac{1}{2} \right)}^{8}} \right]\]\[=1-{{\left( \frac{1}{2} \right)}^{8}}(1+8+8+1)=1-\frac{18}{{{2}^{8}}}=\frac{119}{128}\]
You need to login to perform this action.
You will be redirected in
3 sec
