Multiple choice

$A$ 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

  1. $\displaystyle { \left( \frac { 3 }{ 4 } \right) }^{ 50 }$
  2. $\displaystyle { \left( \frac { 2 }{ 7 } \right) }^{ 50 }$
  3. $\displaystyle { \left( \frac { 1 }{ 8 } \right) }^{ 50 }$
  4. $\displaystyle { \left( \frac { 7 }{ 8 } \right) }^{ 50 }$
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A Correct answer
Explanation

Probability of getting a tail is 1/2. Probability of both NOT getting a tail = 1 - P(both get tails) = 1 - (1/2 * 1/2) = 3/4. For 50 tosses, it is (3/4)^50.

AI explanation

For each simultaneous toss, the probability that both A and B get tails at the same time is 1/2 multiplied by 1/2, which equals 1/4. The probability that they do not get tails at the same time during a single toss is therefore 1 - 1/4 = 3/4. Because the coin tosses are independent events repeated 50 times, the overall probability is found by multiplying this probability by itself 50 times, resulting in ( 3 / 4 ) ^ 50.

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