Question

1.3) (15 points) Exercise 2.1.18. Except there are 106 parts and the numbers in the first column change from 70, 12 to 81, 11 respectively. Discs of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 106 discs are summarized as follows: Shock Resistance High 81 Low Scratch High Resistance Low Let A denote the event that a sample has high shock resistance, and let B denote the event that a disc has high scratch resistance. If a disc is selected at random, determine the number of samples in A nB, A' and A UB. stho nasswerds contain

Answer 1

Let A denote the event that a sample has high shock resistance, and B denote the event that a disc has high scratch resistance.

A' denote the event that a sample has low shock resistance and B' denote the event that a disc has low scratch resistance.

Therefore, the number of samples in following events are

$=> n ( A \cap B) = 81$

$\\n ( A') = 9 + 5 = 14 \\\\ => n(A') = 14$

n(A) = 81 + 11 = 92

n(B) = 81 + 9 = 90

Therefore,

$\\n ( A \cup B) =n(A) + n(B) - n(A \cap B) = 92+ 90-81 \\\\ => n(A \cup B) = 101$