Problem solvers solving problematic problem

Probability Level 3

Four famous brilliant problem solvers have started solving one problematic problem (I will not name those problem solvers). Fifth problem solver (who is a slacker, I will not name this guy either) gave his calculation, on the chance that a problem solver will solve this problematic problem.

The probability that the problem will be solved by

$\begin{array}{c|c}\textrm{Problem solver}&\textrm{Probability of him/her solving the problem}\\ \hline 1\textrm{st}&0.4\\ 2\textrm{nd}&0.5\\ 3\textrm{rd}&0.7\\ 4\textrm{th}&0.9\end{array}$

Now, the slacker is thinking "what is the probability of event where at least one problem solver will solve the problematic problem". It is obvious that slacker is too lazy to work this out, so he asked for Your help. Give the probability in percents, i.e., if the probability is $k$ , give your answer as $100k$ .

The answer is 99.1.

1 solution

Milan Milanic
Apr 21, 2016

Solution:

Let's label slacker's event with $A$ .

Event where each problem solver will fail at solving the problem is $\overline{A}$ .

$P(A) = 1 - P(\overline{A})$

And $P(\overline{A}) = (1 - 0.4) \times (1 - 0.5) \times (1 - 0.7) \times (1 - 0.9) = 0.009$

So $P(A) = 0.991$ or $99.1$ %

Problem solvers solving problematic problem

The answer is 99.1.

1 solution

0 pending reports