Worked solution · Exam P
This Exam P sample reference tests Probability Modeling. Let twin sales have share t. King sales have share 3t and queen sales share (3t+t)/4=t. Normalization gives t=0.2, so king or queen totals 0.8, choice C.
Independent solution
Setup
Let the twin share be t. The king share is 3t, and the queen relation then also gives share t.
Model
Normalize the three mutually exclusive category shares t, 3t, and t to total one.
Compute
Normalization gives t=0.2. King or queen sales therefore have combined share 3t+t=0.8.
Answer
The required probability is 0.80, corresponding to choice C.
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Original practice · fully worked
A café sells small, medium, and large drinks. Large sales are twice small sales, and medium sales equal half of small plus large sales. Find the probability the next drink is medium or large.
Using small share s gives large 2s and medium 1.5s. Normalization gives 4.5s=1, so medium plus large is 3.5/4.5=7/9.
Setup
Let the small-drink share be s. Then large has share 2s and medium has share half of 3s, or 1.5s.
Model
Normalize the three shares s, 1.5s, and 2s, whose coefficients total 4.5.
Compute
Medium and large together account for 3.5 of the 4.5 ratio units, giving 7/9=0.777778.
Answer
The probability of a medium or large drink is 0.7778, corresponding to choice C.
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