A coin is tossed 5 times. What is the probability that the head appears an even number of times?A. $\frac{2}{5}$B. $\frac{3}{5}$C. $\frac{4}{15}$D. $\frac{1}{2}$

Home » A coin is tossed 5 times. What is the probability that the head appears an even number of times?A. B. C. D.

A coin is tossed 5 times. What is the probability that the head appears an even number of times?
A. $\frac{2}{5}$
B. $\frac{3}{5}$
C. $\frac{4}{15}$
D. $\frac{1}{2}$

A coin is tossed 5 times. What is the probability that the head appears an even number of times?
A. $\frac{2}{5}$
B. $\frac{3}{5}$
C. $\frac{4}{15}$
D. $\frac{1}{2}$

Using Bernoulli’s Trial $P($ Success $=x)={ }^{n} C_{x} \cdot p^{x} \cdot q^{(n-x)}$ $x=0,1,2, \ldots \ldots \ldots . .$ and $q=(1-p)$
As the coin is tossed 5 times the total number of outcomes will be $2^{5}$ .
And we know that the favourable outcomes of getting the head even number of times ,successes will be, getting a head,
The probability of success is $\frac{1}{2}$ and of failure is also $\frac{1}{2}$
the probability that head appears an even number of times $=$
$\begin{array}{l} P(0)+P(2)+P(4) \\ ={ }^{5} C_{2}\left(\frac{1}{2}\right)^{2}\left(\frac{1}{2}\right)^{3}+{ }^{5} C_{3}\left(\frac{1}{2}\right)^{3}\left(\frac{1}{2}\right)^{2}+{ }^{5} C_{5}\left(\frac{1}{2}\right)^{5}\left(\frac{1}{2}\right)^{0} \\ \Rightarrow \frac{16}{32}=\frac{1}{2} \end{array}$
Hence, the correct option is d.