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Question

An experiment succeeds twice as often as it fails. The probability of at least $$1$$ successes in the six trials of this experiment is:


A
496729
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B
192729
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C
240729
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D
256729
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Solution

The correct option is D $$\dfrac {256}{729}$$
Let $$p(F) = p\Rightarrow p(S) = 2p$$
$$\because p + 2p = 1\Rightarrow p = \dfrac {1}{3}$$
$$p(x \leq 1) = p(x = 1) + p(x = 0)$$
               $$= ^{6}C_{1} \times \dfrac{1}{3} \times(\dfrac{2}{3})^5 + ^{6}C_{0} \times(\dfrac{2}{3})^6$$
               $$=\dfrac{256}{729}$$


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