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Question

If in a random experiment the probability of getting a success is twice that of a failure, then the probability of getting $$6$$ successes in $$10$$ trials is


A
10C6(13)6(23)4
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B
10C6(23)6(13)4
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C
10C6(14)6(34)4
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D
10C6(34)6(14)4
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Solution

The correct option is A $$^{ 10 }C_{ 6 }{ \left( \cfrac { 2 }{ 3 } \right) }^{ 6 }{ \left( \cfrac { 1 }{ 3 } \right) }^{ 4 }$$
Probability of success$$= \dfrac{2}{3}$$
Probability of failure $$=1-\dfrac{2}{3}= \dfrac{1}{3}$$
Probability of getting 6 successes in 10 trials is $$=^{ 10 }C_{ 6 }{ \left( \dfrac { 2 }{ 3 }  \right)  }^{ 6 }{ \left( \dfrac { 1 }{ 3 }  \right)  }^{ 4 }$$

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