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Difficulty: MediumBasic Single-Event Probability

The table below categorizes 100 analysts at a consulting firm by their department and experience level:

DepartmentJunior (1–3 yrs)Senior (4–7 yrs)Lead (8+ yrs)Total
Technology14161040
Analytics1218535
Operations911525
Total354520100

If one analyst is selected at random from this group, what is the probability that the selected analyst works in the Analytics department or has Lead experience, but NOT both?

Answer: 0.45

Answer

0.45
To find the probability of selecting an analyst who is either in the Analytics department or at the Lead level, but not both, we count the analysts in Analytics who are not Leads (12+18=3012 + 18 = 30) and the analysts at the Lead level who are not in Analytics (10+5=1510 + 5 = 15). The total number of favorable outcomes is 30+15=4530 + 15 = 45. Dividing by the total pool of 100100 analysts yields a probability of 45100=0.45\frac{45}{100} = 0.45.

Step-by-Step Solution

1
Determine the total size of the sample space.
Total analysts N=100N = 100.
Basic probability requires dividing favorable outcomes by total possible outcomes.
2
Calculate the number of analysts satisfying 'Analytics, but NOT Lead'.
Junior Analytics (1212) + Senior Analytics (1818) = 3030.
Excludes the 55 Lead analysts in the Analytics department.
3
Calculate the number of analysts satisfying 'Lead, but NOT Analytics'.
Technology Lead (1010) + Operations Lead (55) = 1515.
Excludes the 55 Lead analysts in the Analytics department.
4
Sum the non-overlapping favorable counts and compute probability.
Favorable outcomes =30+15=45= 30 + 15 = 45; Probability =45100=0.45= \frac{45}{100} = 0.45.
Probability of a single event is defined as Favorable OutcomesTotal Outcomes\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}.

Key Concept

Basic Single-Event Probability from Two-Way Tabular Data with Mutually Exclusive Set Conditions
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Topics

Basic Single-Event Probability

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