Probability Question 143
Question: One coin is thrown 100 times. The probability of coming tail in odd number
[MP PET 2004]
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{8} $
C) $ \frac{3}{8} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let p = Probability of getting tail = $ \frac{1}{2} $
q = Probability of getting head = $ \frac{1}{2} $
Also, $ p+q=1 $ and $ n=100 $
$ \therefore $ Required probability = $ P(X=1)+P(X=3)+…..+P(X=99) $ = $ ^{100}C_1p.q^{99}{{+}^{100}}C_3p^{3}q^{97}+……..{{+}^{100}}C_{99}p^{99}q^{1} $ = $ \frac{{{(p+q)}^{100}}-{{(p-q)}^{100}}}{2}=\frac{1}{2} $ .
BETA
