Question

A box contains 100 shirts of which 88 are good, 8 have minor defects, and 4 have major defects.
Jimmy, a trader, accepts only good shirts. Shaun, another trader, on the other hand, only rejects the shirts with major defects. Find the probability that a shirt selected is: (i) Acceptable to Jimmy (ii) Acceptable to Shaun

• A. (i) 0.88, (ii) 0.96
• B. (i) 0.96, (ii) 0.04
• C. (i) 0.96, (ii) 0.88
• D. (i) 0.88, (ii) 0.12

Answer 1

The correct option is A (i) 0.88, (ii) 0.96

Solution:
Let E be the event of selecting a shirt acceptable to Jimmy.
The number of favorable outcomes for Jimmy is 88.

$P\left(E\right)=\frac{\text{number of outcomes favorable to E}}{\text{total number of outcomes}}$
$=\frac{88}{100}$

$=0.88$

Let F be the event of selecting a shirt acceptable to Shaun.
The number of favorable outcomes for Shaun = 88 + 8 = 96

$P\left(F\right)=\frac{\text{number of outcomes favorable to F}}{\text{total number of outcomes}}$

$=\frac{96}{100}$

$=0.96$