A fair coin is tossed 6 times. What is the probability of getting at least 3 heads?A. $\frac{11}{16}$B. $\frac{21}{32}$C. $\frac{1}{18}$D. $\frac{3}{64}$

Home » A fair coin is tossed 6 times. What is the probability of getting at least 3 heads?A. B. C. D.

A fair coin is tossed 6 times. What is the probability of getting at least 3 heads?
A. $\frac{11}{16}$
B. $\frac{21}{32}$
C. $\frac{1}{18}$
D. $\frac{3}{64}$

A fair coin is tossed 6 times. What is the probability of getting at least 3 heads?
A. $\frac{11}{16}$
B. $\frac{21}{32}$
C. $\frac{1}{18}$
D. $\frac{3}{64}$

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 thrown 6 times the total number of outcomes will be $2^{6}$ .
And we know that the favourable outcomes of getting at least 3 successes will be, getting a head The probability of success is $\frac{1}{2}$ and of failure is also $\frac{1}{2}$
${ }^{6} \mathrm{C}_{3}\left(\frac{1}{2}\right)^{3}\left(\frac{1}{2}\right)^{3}+{ }^{6} \mathrm{C}_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{2}+{ }^{6} \mathrm{C}_{5}\left(\frac{1}{2}\right)^{5}\left(\frac{1}{2}\right)^{1}+{ }^{6} \mathrm{C}_{6}\left(\frac{1}{2}\right)^{6}\left(\frac{1}{2}\right)^{0}$
$\Rightarrow \frac{21}{32}$
Hence, the correct option is b.