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

Question

An unbiased coin is tossed 6 times, then the probability that 3 textrd head appears on the 6 textth trial, is (A) (5/16) (B) (5/32) (C) (5/8) (D) (5/64)

Tardigrade Admin · Accepted Answer

The probability of getting head is (1/2) and of tail is also (1/2) . Hence, the probability of getting 5 heads and 1 tail in a coin toss of 6 times is 5 C2((1/2))5 × (1/2)=(5/32)

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

$\frac{5}{16}$

$\frac{5}{32}$

$\frac{5}{8}$

$\frac{5}{64}$

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
$^{5} C_{2} (\frac{1}{2})^{5} \times \frac{1}{2} = \frac{5}{32}$

Q. An unbiased coin is tossed 6 times, then the probability that 3rd head appears on the 6th trial, is

165​

325​

85​

645​