When Julia is writing a first draft, there is 0.7 probability that there will be

Cheyanne Leigh 2021-10-02 Answered

The chances that Julia will have no spelling mistakes on a page she is writing are 0.7. One day, Julia writes a first draft that is 4 pages long. 
Assuming that Julia is equally likely to have a spelling mistake on each of the 4 pages, what is the probability that she will have no spelling mistakes on at least one of them? 
P(at least one without mistakes)=_

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Expert Answer

irwchh
Answered 2021-10-03 Author has 102 answers

Step 1 
Given Data : Probability of no spelling mistakes on a page P (no mistake) =0.7 
To Find : The probability of at least one without errors 
Let X be the number of pages among these 4 pages which Julia writes with zero mistakes 
Binomial Probability : The probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes. It express as : 
Binomial Probability =nCxpx(1p)nx 
Step 2 
In the given question we have : 
Probability p=0.7 
n is the total number of pages i.e. n=4 
To find the at-least one page out of 4 pages with zero mistakes, X1 
Substitute the value of p,n and X in the expression of Binomial probability: 
Step 3 
Binomial Probability =nCxpx(1p)nx 
Probability for (X=x)=4Cxpx(1p)4x 
for x1 
P(x1)=1P(x=0) 
P(x1)=14Cx(0.7)x(10.7)4xp(x1)=14C0(0.7)0(0.3)40 
P(x1)=14!0!(40)!×1×(0.3)4 
P(x1)=11×1×0.0081 
P(x1)=10.0081 
P(x1)=0.9919 
So, Probability of at least one page with zero mistake is 0.9919 
Round of to the nearest hundredth 0.9919~0.99 
Answer: 
P(at-least one without mistake) =0.99

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