\(A, B\) and \(C\) can solve \(50 \%, 60 \%\) and \(70 \%\) of the sums from a book. If one sum from that book is given them to solve then probability that the sum will be solved is (a) \(0.94\) (b) \(0.06\) (c) \(0.47\) (d) None

Short Answer

Expert verified
The short answer is: The probability that the sum will be solved by at least one of them is \(0.94\).

Step by step solution

01

Write down the given probabilities of solving the problem

The three individuals have the probabilities of \(50 \%\), \(60 \%\) and \(70 \%\) respectively to solve the problem. Let's write it down: \(P(A) = 0.5\) \(P(B) = 0.6\) \(P(C) = 0.7\)
02

Calculate the probability of not solving the problem

Now we will calculate the probability that each individual will not solve the problem: \(P(A') = 1- P(A) = 1-0.5 = 0.5\) \(P(B') = 1- P(B) = 1-0.6 = 0.4\) \(P(C') = 1- P(C) = 1-0.7 = 0.3\)
03

Calculate the probability of all three not solving the problem

Now we need to find the probability that all three of them will not solve the problem. We will multiply the probabilities of the complementary events: \(P(A' \cap B' \cap C') = P(A') * P(B') * P(C') = 0.5 * 0.4 * 0.3 = 0.06\)
04

Calculate the probability of at least one solving the problem

Now, we will find the probability that at least one of them will solve the problem which is the complementary event we calculated in step 3: \(P(\text{at least one solves}) = 1 - P(A' \cap B' \cap C') = 1 - 0.06 = 0.94\)
05

Identify the answer

In the options provided, the correct answer is: (a) \(0.94\) So, the probability that the sum will be solved by at least one of them is \(0.94\).

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