Question

An experiment succeeds thrice as after it fails. If the experiment is repeated 5times, what is the

probability of having no success at all?​

Answer 1

Given : An experiment succeeds thrice as often as  it fails. 4the experiment is repeated 5times,  

To Find :  probability of having no success at all

Solution:

An experiment succeeds thrice as often as  it fails

Let say probability of fail = x

probaility of success = 3x

Probability of Fail +Success = 1

=> x + 3x = 1

=> 4x = 1

=> x = 1/4

probability of fail = 1/4

probability of success = 3/4

experiment is repeated 5times

n = 5

probability of having no success at all   =  all fails  = ⁵C₅(3/4)⁰(1/4)⁵ = 1/1024

1/1024  is the probability of having no success at all

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Answer 2

Answer:

1/1024

Step-by-step explanation:

An experiment succeeds thrice as often as it fails.

Let X is the probability of fail.

Thus the probability of success = 3/4

And the probability of fail = 1/4

If the experiment is repeated five times, so n = 5

Here r = 0 and ( n - r ) = 5

Probability of having no success at all = all fails

= 5C0(3/4)^0(1/4)^5

= 1/1024