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

For each toss there are four choice
(i) $A$ gets head, $B$ gets head
(ii) $A$ gets tail, $B$ gets head
(iii) $A$ gets head, $B$ gets tail
(iv) $A$ gets tail, $B$ gets tail
Thus, exhaustive number of ways $=4^{50}$.
Out of the four choice listed above (iv) is not favorable to the required event in a toss.
Therefore favorable number of cases is $3^{50}$
Hence, the required probability $={\left(\frac{3}{4}\right)}^{50}$