The number of typing errors made by a typist has a Poisson distribution with an

Question

The number of typing errors made by a typist has a Poisson distribution with an average of 0.2 errors per line. If more than five errors appear on a given page, the typist must retype the whole page. (a) What is the probability that a randomly selected page that contains 20 lines does not need to be retyped? (b) What is the probability that a randomly selected page that contains 30 lines has exactly four typos? Two fair dice are thrown. (a) Find the probability of getting a sum of 5 or more. (b) Find the probability of getting a sum of 5 or more given than the sum is even. (c) Are the two events "sum of 5 or more" and "sum is even" independent?

Explanation / Answer

Q.2 (a) THe total possibilities = 6 * 6 = 36

Total possibilities og getting a sum of 5 or more. = Poss (5 or more)

Here Po(5) = 4, Po(6) = 5, Po(7) = 6 , Po(8) = 5 , Po(9) = 4 , Po(10) = 3, Po( 11) = 2 , Po(12) = 1

so all possibilities = sum of all possibilities = 30

so Pr ( sum of 5 or more) = 30/36 = 5/6

(b) Here it is given that sum is even so the sum should be 2,4,6,8, 10, 12

so total possiblities = Po(2) + Po(4 ) + Po(6) + Po(8) + Po(10) + Po(12)

= 1 + 3 + 5 + 5 + 3 + 1 = 18

so out of which sum 5 or more are events (6,8,10,12)

so total possiblities = Po(6) + Po(8) + Po(10) + Po(12)

= 5 + 5 + 3 + 1 = 14

so Pr( sum of 5 or more given that the sum is even) = 14/ 18 = 7/9

(c) Are the two events " sum of 5 or more" Let say A and " sum is even" Let say B independent?

so Pr(A) = 5/6

and Pr( B) = 1/2

so if these events are independent then Pr( A and B) = Pr(A) x Pr(B)

Pr( A and B) = 7/9

Pr(A) x Pr(B) = 5/6 * 1/2 = 5/12

so no these two events are not independent.

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