Practicing Success
A fair coin is tossed a fixed number of times . If the probability of getting 7 heads is equal to getting 9 heads, then the probability of getting 2 heads is, |
$15 / 2^8$ $2 / 15$ $15 / 2^{13}$ none of these |
$15 / 2^{13}$ |
Let coin was tossed 'n' times and X be the random variable representing the number of head appearing in 'n' trials. $P(X=7)=P(X=9) \Rightarrow{ }^n C_7(1 / 2)^7(1 / 2)^{n-7}={ }^n C_9(1 / 2)^{n-9} \times(1 / 2)^9$ $\Rightarrow{ }^n C_7={ }^n C_9 \Rightarrow n=16$ Now $P(X=2)={ }^{16} C_2(1 / 2)^2(1 / 2)^{14}=\frac{{ }^{16} C_2}{2^{16}}=\frac{16.15}{2^{17}}=\frac{15}{2^{13}}$ |