In probability theory and statistics, two events are said to be mutually exclusive if they cannot occur at the same time. In other words, the occurrence of one event excludes the occurrence of the other.
For example, consider the event of tossing a coin. The two possible outcomes (events) are:
- The coin lands heads up.
- The coin lands tails up.
These two events are mutually exclusive because both cannot happen at the same time. If the coin lands heads up, it cannot also land tails up, and vice versa.
Let’s consider a more practical example related to weather conditions. Suppose you are planning an outdoor event and are considering two weather conditions: rainy (Event R) and sunny (Event S). In this scenario, it’s reasonable to consider the events “rainy” and “sunny” as mutually exclusive. This is because it cannot be both rainy and sunny at the same time (neglecting the rare case of sun showers).
Quizzes
In a manufacturing process, the probability of a machine producing a defective part is 0.05, and the probability of it producing a non-defective part is 0.95. Are these events mutually exclusive?
A. Yes
B. No
Show answer
Answer:
A. Yes
Two engineers are working on separate projects. The probability that Engineer A completes their project on time is 0.8, and the probability that Engineer B completes their project on time is 0.7. Are the events of Engineer A completing on time and Engineer B completing on time mutually exclusive?
A. Yes
B. No
Show answer
Answer:
B. No
In a reliability test, a component can either fail due to fatigue or corrosion, but not both. Are the events of failure due to fatigue and failure due to corrosion mutually exclusive?
A. Yes
B. No
Show answer
Answer:
A. Yes
In a market, a company can either achieve a profit or a loss in a given financial period. Are these two outcomes mutually exclusive?
A. Yes
B. No
Show answer
Answer:
A. Yes
An investor is choosing between investing in stocks or bonds. The decision is based on market conditions, and the investor can invest in both simultaneously. Are the events of investing in stocks and investing in bonds mutually exclusive?
A. Yes
B. No
Show answer
Answer:
B. No
Quiz with Calculations
An engineer is testing two independent systems, A and B. The probability that system A fails is 0.2, and the probability that system B fails is 0.3. What is the probability that both systems fail simultaneously?
Show answer
Calculation:
Answer:
0.06
A company can either introduce a new product (Event A) with a probability of 0.4 or enter a new market (Event B) with a probability of 0.5. If these events are mutually exclusive, what is the probability that the company either introduces a new product or enters a new market?
Show answer
Calculation:
Answer:
0.9
An investor is deciding between investing in stock A with a probability of 0.6 and stock B with a probability of 0.7. Assuming these events are not mutually exclusive and the probability of investing in both stocks is 0.3, what is the probability that the investor invests in either stock A or stock B?
Show answer
Calculation:
Answer:
1.0
A test for a particular disease has a 0.02 probability of yielding a false positive and a 0.01 probability of yielding a false negative. What is the probability that a test either yields a false positive or a false negative, assuming these events are mutually exclusive?
Show answer
Calculation:
Answer:
0.03
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