Question

A and B toss a fair coin each simultaneously 50 times. The probability that both of them will not get a 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

Hint: First of all, determine the maximum possible cases when both the coins are tossed simultaneously. After that, determine the possible cases when both the coins are tossed simultaneously 50 times. And then determine the probability that both the coins will not get the tail at the same toss out of the total number of possible cases. Hence, we will get a suitable answer.

Complete step by step solution: 
As given in the question, Coin A and B are tossed simultaneously 50 times. Now we know that each coin has a maximum of two possible cases, that is, maybe the tail or maybe the head. Hence we can conclude that the maximum possible cases when the two coins are tossed simultaneously,
\[ \Rightarrow 4\]
Now, when both the coins are tossed simultaneously 50 times, then possible cases will be,
\[ \Rightarrow {4^{50}}\]
Four possible cases will be such as,
Case 1: Coin A gets head, coin B gets head
 Case 2: Coin A gets tail, coin B gets tail
Case 3: Coin A gets head, coin B gets tail
Case 4: Coin A gets tail, coin B gets head
So, now according to the question, we have to determine the probability that both the coins will not get tails in 50 attempts.
If both the coins will not get the tail, then three cases will be selected. Therefore, the probability of the event will be,
\[ \Rightarrow {3^{50}}\]
Now, the probability that both the coins will not get the tail out of 4 possible cases in 50 attempts,
\[ \Rightarrow \frac{{{3^{50}}}}{{{4^{50}}}}\]
\[ \Rightarrow {\left( {\frac{3}{4}} \right)^{50}}\]
Now, the final answer will be \[{\left( {\frac{3}{4}} \right)^{50}}\].
Therefore, the correct option is (A)..

Note: The first point to keep in mind is to determine the maximum possible cases of an event occurring and then we will see what probability we have to find.