First slide

Theorems of 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

$(3 / 4)^{50}$
B

$(2 / 7)^{50}$
C

$(1 / 8)^{50}$
D

$(7 / 8)^{50}$

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 rail
(iv) A gets tail, B gets tail
Thus, exhaustive number of ways is $4^{50}$ . Out of the four choices 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 is ( $(3 / 4)^{50} .$

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