Question 1198546: a What is the probability that the painting and building of the scenery takes exactly
13 days?
b What is the probability that the three tasks together take exactly 19 days?
A school is staging a musical and must have the scenery and programs ready for
the opening night. The following probabilities are estimated for the duration of the
activities
Task 5 days 6 days 7 days
Build scenery 0.1 0.45 0.45
Paint scenery 0.3 0.4 0.3
Print programs 0.5 0.3 0.2
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **a) Probability that painting and building the scenery takes exactly 13 days**
* **Possible combinations:**
* Build: 5 days, Paint: 8 days
* Build: 6 days, Paint: 7 days
* Build: 7 days, Paint: 6 days
* **Calculate probabilities:**
* Build: 5 days, Paint: 8 days: 0.1 (Build) * 0 (Paint) = 0
* Build: 6 days, Paint: 7 days: 0.45 (Build) * 0.3 (Paint) = 0.135
* Build: 7 days, Paint: 6 days: 0.45 (Build) * 0.4 (Paint) = 0.18
* **Total probability:** 0 + 0.135 + 0.18 = 0.315
**Therefore, the probability that painting and building the scenery takes exactly 13 days is 0.315.**
**b) Probability that all three tasks together take exactly 19 days**
* **Possible combinations:**
* Build: 5 days, Paint: 6 days, Print: 8 days
* Build: 5 days, Paint: 7 days, Print: 7 days
* Build: 6 days, Paint: 5 days, Print: 8 days
* Build: 6 days, Paint: 6 days, Print: 7 days
* Build: 6 days, Paint: 7 days, Print: 6 days
* Build: 7 days, Paint: 5 days, Print: 7 days
* Build: 7 days, Paint: 6 days, Print: 6 days
* **Calculate probabilities for each combination:**
* (0.1 * 0.4 * 0.2) + (0.1 * 0.3 * 0.2) + (0.45 * 0.3 * 0.2) + (0.45 * 0.4 * 0.2) + (0.45 * 0.3 * 0.3) + (0.45 * 0.3 * 0.2) + (0.45 * 0.4 * 0.3) = 0.231
**Therefore, the probability that all three tasks together take exactly 19 days is 0.231.**
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