Question

Two person A and B have 16 and 15 fair coin
respectively. If both of them tosses all the coin
then probability that A gets more head than B is
p then the value of 16p is​

Answer 1

Given that:

Two persons A and B have 16 and 15 fair coins  respectively.

All the coins are tossed.

Probability that A gets more head than B is p.

To find:

value of 16p = ?

Solution:

First of all, let us have a look at the formula for Probability of an event E.

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

For a fair coin scenario, Probability of getting a head or tail, has number of favorable cases as 1 and total number of cases are 2.

So,

$P(Heads) = P (Tails) = \dfrac{1}2$

Now, let us suppose A and B both had same number of coins i.e. 15 coins each with A and B.

Then getting number of heads for A and B are equally likely.

Now, it is given that A has 1 more coin than that of B.

So, probability that A will have more number of heads will be equal to the getting a head on the 1 extra coin that A has.

So, probability p = $\bold{\frac{1}{2}}$.

Hence, the value of 16p = $16\times \frac{1}{2} = \bold8$.

So, answer is 8.