**Probability ncert solutions Chapter 15 Exercise 15.1 Question 9**

**9. **A box contains 5 red marbles, 8 white marbles, and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be

(i) red? (ii) white? (iii) not green?

**Solution**

**(i)**

Let E be the Event that selected marble is red.

Number of possible outcomes favorable to event E=5 {Because there are 5 red marbles}

Total number of possible outcomes=5+8+4=17 {Total number of balls}

Probability that the selected marble is red=(Number of outcomes favorable to Event E)/Total number of possible outcomes**=5/17**

**(ii)**

Let E1 be the event that selected marble is white.

Number of possible outcomes favorable to event E1=8 {Because there are 8 white marbles}

Total number of possible outcomes=5+8+4=17 {Total number of balls}

Probability that the selected marble is white=(Number of outcomes favorable to Event E1)/Total number of possible outcomes**=8/17**

**(iii)**

Continuing from part **(i)** and **(ii)**

Let E2 be the Event that selected marble is not green.

The ball cannot be green if it is either red or white. Therefore, Event E2 will happen if there is either Event E or event E1.

The number of possible outcomes favorable to Event E2=5+8=13 (Number of red balls + number of white balls)

Total number of possible outcomes=5+8+4=17 {Total number of balls}

**=13/17**