Question

In a game called 'odd man out', $m(m>2)$ persons toss a coin to determine who will buy refreshment for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is

• A. $1/2m$
• B. $m/2^{m-1}$
• C. $2/m$
• D. none of these

Answer 1

The correct option is B $m/2^{m-1}$

Let us represent the person as $P_1$ , $P_2$ , $P_3$ , $Pm.$

For each person we have 2 outcome,

So, total outcomes $=2^m$

Favorable outcomes:

$1.$ One gets tail rest $\to$ Head

$2.$ One get head test $\to$ Tail

No. of ways $m\times 1$ ($m=$ because in people).

Also for second condition we have $m$ ways.

Total favorable ways $=\frac{2m}{{20}^m}=m/2^{m-1}$

Hence, answer is $m/2^{m-1}.$