Answer:
0.994
Explanation:
the easiest way for a problem like this is to say :
the probability that it gets solved in any form and way is the opposite of none of them can solve it.
the probabilities to not solve the problem are
1 - 0.8 = 0.2
1 - 0.9 = 0.1
1 - 0.7 = 0.3
the probability that all the of them fail is
0.2 × 0.1 × 0.3 = 0.006
the probability that the problem gets solved is the opposite of that :
1 - 0.006 = 0.994
we could do it structured as well :
it is the probability that
student 1 solved it but not students 2 and 3.
0.8 × 0.1 × 0.3 = 0.024
or
student 2 solved it but not students 1 and 3.
0.9 × 0.2 × 0.3 = 0.054
or
student 3 solved it but not students 1 and 2.
0.7 × 0.2 × 0.1 = 0.014
or
student 1 and 2 solved it but not student 3.
0.8 × 0.9 × 0.3 = 0.216
or
student 1 and 3 solved it but not student 2.
0.8 × 0.7 × 0.1 = 0.056
or
student 2 and 3 solved it but not student 1.
0.9 × 0.7 × 0.2 = 0.126
or
student 1, 2 and 3 solved it.
0.8 × 0.9 × 0.7 = 0.504
and now all "or" are added probabilities. so, we add them all up :
0.024 + 0.054 + 0.014 + 0.216 + 0.056 + 0.126 + 0.504 =
0.994
so, we were correct already in the first place.