Combination / Cost / Probability
1 / 870 /.62
2 / 600 / .65
3 / 540 / .72
4 / 500 / .8
5 / 400 / .82
6 / 320 / .82
7 / 300 / .83
8 / 230 / .86
9 / 200 / .86
10/ 170 / .92
Each item from 1 to 10 is an event with a probability of occurrence associated with it. Probabilities of each item are independent of each other.
Find a subset of these items such that the combined cost (sum of individual costs) is minimized under the constraint that the probability of all the events of this subset occuring (obtained by multiplying their individual probabilities) is less than 0.25.
Please state the subset selected, the probability and the total cost.
Thanks!