The probability of aren to solve a problem is 0.3 and the probability of alice to solve the same problem is 0.6 . Find the probability that the problem is solved by none of them?
The answer is 0.28 (or 28%).
The probability that Aren does NOT solve the problem is 0.7.
The probability that Alice does NOT solve the problem is 0.4.
But the question is asking for the probability that neither solves the problem, so it requires you to multiply 0.7 by 0.4, which gives you 0.28. Another way to ask the question is "what is the probability that Aren does not solve the problem AND Alice does not solve the problem". In such questions, the multiplication operator is a substitute for the word "and".
You can also think about the three other options.
- The probability that Aren solves and Alice does not = 0.3*0.4=0.12.
- The probability that Aren does not solve and Alice solves = 0.7*0.6=0.42.
- The probability that both solve = 0.3*0.6=0.18.
If you add up all four, it should equal 1 (this is a good check that you did it right), and it does: 0.28+0.12+0.42+0.18=1.