Multiple choice

Two persons A and B toss a coin 50 times each together. Find the probability both of them get tails at the same time.

  1. $\left ( \dfrac{1}{2} \right )^{50}$
  2. $\left ( \dfrac{1}{4} \right )^{100}$
  3. $\left ( \dfrac{1}{4} \right )^{50}$
  4. $\left ( \dfrac{1}{3} \right )^{50}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Each toss is independent. Probability of tails for one person is 1/2. Probability both get tails in one toss is 1/2 * 1/2 = 1/4. For 50 tosses, it is (1/4)^50.

AI explanation

For each of the 50 rounds, both A and B must get tails for them to get tails at the same time. The probability of A getting a tail is 1/2, and the probability of B getting a tail is 1/2. Because their coin tosses are independent events, the probability that both get a tail in a single round is 1/2 times 1/2, which is 1/4. For this to happen in all 50 rounds, we raise this probability to the power of 50, giving (1/4)^50.

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