Question

A book of 500pages contains 500 mistakes . find the probability that there are atleast 4 mistakes in a randomly selected page

Answer 1

Answer: $\frac{494}{500}$

Step-by-step explanation:

• We calculate probability by dividing the number of favourable outcomes by number of total outcomes.
• Given,500 pages contains 500 mistakes.
• To calculate the probability of getting 4 mistakes in a page.
• We need to apply the complement method here and calculate the probability of getting 0,1,2 and 3 errors and then add the probability of getting 4 errors to get the total probability.
• According to theorem, P(A)+P(A')=1

        Where P(A)=Probability of getting 4 errors

         P(A')=Probability of not getting 4 i.e., getting 0,1,2 and 3 errors

• P(0)=0
• P(1)=$\frac{1}{500}$
• P(2)=$\frac{2}{500}$
• P(3)=$\frac{3}{500}$
• Now, applying the theorem P(A)=1-[P(0)+P(1)+P(2)+P(3)]

                                                   ⇒ $P(A)=1-[0+\frac{1}{500}+\frac{2}{500}+\frac{3}{500} ]$

                                                   ⇒$P(A)=1-\frac{6}{500}$

                                                  ∴ P(A)=$\frac{494}{500}$

• Hence,the probability of getting 4 errors in 1 page is $\frac{494}{500}$.

#SPJ3