You are funding your own business despite the fact that it is loosing. With a business...

You are funding your own business despite the fact that it is loosing. With a business success rate of 50%, what is the probabilityof having less than 2 business sucesses before 4 looses

Expert Solution

Ans Here we need to find the probability that the number of success is less than 2 before 4 looses which can be 0 or 1.

So let the number of business success before 4 looses be denoted by X.

So probability that X = 0 means of the occurance of event that all the first 4 are looses

So P( X = 0 ) = P( 1 is lose and 2 is lose and 3 is lose and 4 is lose ) and since each of them are independent we can write this = P( 1 is lose ) * P(2 is lose) * P(3 is lose) * P(4 is lose)

= 0.5⁴ = 0.0625

And Probability that X = 1 means among the first one is success and the rest 4 is lose.

Now probability of one success and 4 loss = 0.5⁵ but we can choose one out of the five positions for the success which can be done in ways = 5 ways but it cannot be in last place so it can have 4 patterns

So P(X = 1) = 4 * 0.5⁵ = 0.125

So the required probability is P(X=0) + P(X=1) = 0.0625 + 0.125 = 0.1875

Please upvote if found helpful or do comment for any further doubts.

orchestra answered 2 years ago

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