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
B
192729
C
240729
D
256729

Solution

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

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