A task is assigned to four individuals A, B, C, and D. The probability of completing the task by each person is given as follows:Person A has a 1/5 chance of completing the task.Person B has a 3/10 chance of completing the task.Person C has a 2/7 chance of completing the task.Person D has a 1/4 chance of completing the task.What is the probability that the task will be completed?
Question
A task is assigned to four individuals A, B, C, and D. The probability of completing the task by each person is given as follows:Person A has a 1/5 chance of completing the task.Person B has a 3/10 chance of completing the task.Person C has a 2/7 chance of completing the task.Person D has a 1/4 chance of completing the task.What is the probability that the task will be completed?
Solution
The probability that the task will be completed can be found by first finding the probability that the task will not be completed by each individual, and then multiplying these probabilities together to find the total probability that the task will not be completed. This is because the events are independent, meaning the outcome of one does not affect the outcome of the others.
- The probability that person A will not complete the task is 1 - 1/5 = 4/5.
- The probability that person B will not complete the task is 1 - 3/10 = 7/10.
- The probability that person C will not complete the task is 1 - 2/7 = 5/7.
- The probability that person D will not complete the task is 1 - 1/4 = 3/4.
Multiply these probabilities together to find the total probability that the task will not be completed:
4/5 * 7/10 * 5/7 * 3/4 = 0.6
Therefore, the probability that the task will be completed is 1 - 0.6 = 0.4 or 40%.
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