A fair coin is tossed 11 times. What is the probability that only the first two

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Question
A fair coin is tossed 11 times. What is the probability that only the first two tosses will yield heads ?
Options
A. (1/2)^11
B. (9)(1/2)
C. (11C2)(1/2)^9
D. (1/2)

Correct Answer

(1/2)^11

Explanation

Probability of occurrence of an event,

P(E) = Number of favorable outcomes/Numeber of possible outcomes = n(E)/n(S)

? Probability of getting head in one coin = �,

? Probability of not getting head in one coin = 1- � = �,

Hence,

All the 11 tosses are independent of each other.

? Required probability of getting only 2 times heads = ${(\frac{1}{2})}^{2} � {(\frac{1}{2})}^{9} = {(\frac{1}{2})}^{11}$