An experiment succeeds twice as often as it fails. What is the probability that

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An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?

Options:

A . 80232

B . 1753

C . 80213

D . 80243

Answer: Option D
:
D
An experiment succeeds twice as often as it fails. So, the probability of success is

\frac{2}{3}

and the probability of failure is

\frac{1}{3}

.
In the next 5 trials, the experiment needs to succeed in 4 out of the 5 trials. 4 out of 5 trials can be selected in

^{5}

C

_{4}

= 5 ways.
So, required probability = 5 ×

{(\frac{2}{3})}^{4}

×

(\frac{1}{3})

=

\frac{80}{243}

Hence option (d)

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