Question

The chance for A to solve a problem is 50%, B to solve a problem is 60% and C to
solve a problem is 80%. What is the probability that the problem is solved once al
the three try?

Answer 1

Answer:

3/4

Step-by-step explanation:

P(Problem will be solved)

=1−P(Problem will not be solved by A,B and C)

=1−[(1−

2

1

)(1−

3

1

)(1−

4

1

)]

=1−

2

1

×

3

2

×

4

3

=1−

4

1

=

4

3

Hence, D is the correct option.

Answer 2

Concept:

Probability is the chance of occurrence of a given event. It is defined as

P(Y) + P(not Y)=1

here, Y is an outcome in an event

P(Y) is the probability of the outcome Y in the event.

P(not Y) is the probability of not getting the outcome Y in the event.

If I,J,K are independent events, then the probability of outcome from I,J,K events are

P(I∩J∩K) = P(I)×P(J)×P(K)

Given

Chances of A to solve the problem = 50%

Chances of B to solve the problem = 60%

Chances of C to solve the problem = 80%

Find

Probability that the problem will be solved by any one of them.

Solution

Probability of A to solve the problem $=\frac{50}{100}$

                                                              $=\frac{1}{2}$

Probability of A not solve the problem $=1-\frac{1}{2}$

                                                                $=\frac{1}{2}$

Probability of B solving the problem $=\frac{60}{100}$

                                                              $=\frac{3}{5}$

Probability of B not solve the problem $=1-\frac{3}{5}$

                                                                $=\frac{2}{5}$

Probability of C solving the problem $=\frac{80}{100}$

                                                              $=\frac{4}{5}$

Probability of C not solve the problem $=1-\frac{4}{5}$

                                                                $=\frac{1}{5}$

Probability of solving the problem by any one of them is

                                  = 1 - (none of them solved the problem)

                                  = 1 - (P(not A ∩ not B ∩ not C))

                                  $=1 - (\frac{1}{2} *\frac{2}{5}*\frac{1}{5})$        

                                  $=1-\frac{1}{25}$

                                  $=\frac{24}{25}$    

Hence, the probability of solving the problem by any one is  $=\frac{24}{25}$