Question

$A$and $B$toss a fair coin each simultaneously $50$ times.The probability that both of them will not get tail at the same toss is

• A. ${\left(\frac{3}{4}\right)}^{50}$
• B. ${\left(\frac{2}{7}\right)}^{50}$
• C. ${\left(\frac{1}{8}\right)}^{50}$
• D. ${\left(\frac{7}{8}\right)}^{50}$

Answer 1

The correct option is A

${\left(\frac{3}{4}\right)}^{50}$

Explanation for the correct options:

Step 1. Find the total number of ways :

Given that $A$and $B$toss a fair coin each simultaneously $50$ times.

For each toss, there will be $4$choices.

Choice$1$: $A$ gets head, $B$ gets head

Choice$2$: $A$ gets tail, $B$ gets head

Choice$3$: $A$ gets head, $B$ gets tail

Choice$4$: $A$ gets tail, $B$ gets tail.

Therefore, the total number of ways $=4^{50}$

Step 2. Find the required probability :

Out of four choices, choice $\left(4\right)$ is not favorable.

Therefore, the favorable number of ways $=3^{50}$

Hence, the required probability

$=\frac{3^{50}}{4^{50}}$ $\left[\because Probability=\frac{fovorablecases}{Totalcases}\right]$

$={\left(\frac{3}{4}\right)}^{50}$

Hence, option(A) is the correct answer.