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  4. An unbiased coin is tossed 6 times, then the probability that 3 textrd head appears on the 6 textth trial, is

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Q. An unbiased coin is tossed $6$ times, then the probability that $3^{\text{rd}}$ head appears on the $6^{\text{th}}$ trial, is

NTA AbhyasNTA Abhyas 2022

Solution:

The probability of getting head is $\frac{1}{2}$ and of tail is also $\frac{1}{2}$ .
Hence, the probability of getting $5$ heads and $1$ tail in a coin toss of $6$ times is
${ }^{5} C_{2}\left(\frac{1}{2}\right)^{5} \times \frac{1}{2}=\frac{5}{32}$