First slide

Introduction to probability

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

Moderate

A

${(\frac{3}{4})}^{50}$
B

${(\frac{2}{7})}^{50}$
C

${(\frac{1}{8})}^{50}$
D

${(\frac{7}{8})}^{50}$

Solution

For each toss, there are four choices:
(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 is 4⁵⁰. Out of the four choices listed above, (iv) is not favorable to the required event in a toss. Therefore, favorable number of cases is 3⁵⁰. Hence, the required probability is (3/4)⁵⁰.

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