Step 1: Finding the average number of errors The typist makes 1 mistake for every 10 pages. For 40 pages, expected errors =‌
40
10
=4. Step 2: Setting up the Poisson distribution We use the Poisson formula to find the chance of getting up to 2 errors when the average ( λ ) is 4 . P(X=k)=‌
e−44k
k!
Step 3: Find probability of at most 2 errors We need to calculate P(X≤2)=P(X=0)+P(X=1)+P(X=2) : ‌P(X=0)=‌
e−4⋅40
0!
=e−4 ‌P(X=1)=‌
e−4⋅41
1!
=4e−4 ‌P(X=2)=‌
e−4⋅42
2!
=8e−4 Add them up: p=e−4+4e−4+8e−4=13e−4 Step 4: Multiply by e2 as asked in the question e2p=13e−4×e2=13e−2