Out of three bags that each contains 10 marbles :

  • Bag 1 has 6 red and 4 blue marbles
  • Bag 2 has 5 red and 5 blue marbles.
  • Bag 3 has 2 red and 8 blue marbles.

What is the Probability of choosing a red marble?

  • Option 1)

    \frac{11}{300}

  • Option 2)

    \frac{13}{300}

  • Option 3)

    \frac{17}{300}

  • Option 4)

    \frac{7}{300}

 

Answers (1)

As we learned 

 

The law of Total Probability -

Let S be the sample space and E1, E2, ......En be n mutually exclusive and exhaustive events associated with a random experiment.

- wherein

\Rightarrow P\left ( A \right )= P\left ( A\cap E_{1} \right )+P\left ( A\cap E_{2} \right )+\cdots +P\left ( A\cap E_{n} \right )

\Rightarrow P\left ( A \right )= P\left ( E_{1} \right )\cdot P\left ( \frac{A}{E_{1}} \right )+P\left ( E_{2} \right )\cdot P\left ( \frac{A}{E_{2}} \right )+\cdots P\left ( E_{n} \right )\cdot P\left ( \frac{A}{E_{n}} \right )

where A is any event which occurs with E1, E2, E3......En.

 

 P\left ( \frac{R}{B_{1}} \right )=0.6\: ;\: P\left ( \frac{R}{B_{2}} \right )=0.2

Thus P\left ( R \right )=\frac{1}{3}\left ( 0.6 \right )+\frac{1}{3}\left ( 0.5 \right )+\frac{1}{3}\left ( 0.2 \right )

=\frac{0.11}{3}

=\frac{11}{300}

 


Option 1)

\frac{11}{300}

Option 2)

\frac{13}{300}

Option 3)

\frac{17}{300}

Option 4)

\frac{7}{300}

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