A problem in mathematics is given to three students A,B,C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is

  • Option 1)

    3/4

  • Option 2)

    1/2

  • Option 3)

    2/3

  • Option 4)

    1/3

 

Answers (1)
V Vakul

As we learnt in 

Complementary events -

Let S be the sample space  for a random experiment and let E be the event then complement of event E is 

S-n\left ( E \right )= \left n( E{}' \right )

\therefore n\left ( E \right ) + n\left ( E{}' \right )= n\left ( S \right )

- wherein

where E' contains those element which E does not contain.

 

 P\bar{(A)}=\frac{1}{2},\ P\bar{(B)}=\frac{2}{3},\ P\bar{(C)}=\frac{3}{4}

Probability that quostion is not solved=P\left ( \bar{A} \right ) P\left ( \bar{B} \right ) P\left ( \bar{C} \right )=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}=\frac{1}{4}

P (question is solved) =1-P\left ( \bar{A} \right ) P\left ( \bar{B} \right ) P\left ( \bar{C} \right )

=1-\frac{1}{4}

=\frac{3}{4}


Option 1)

3/4

Correct option

Option 2)

1/2

Inorrect option

Option 3)

2/3

Inorrect option

Option 4)

1/3

Inorrect option

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