A box contains 5 red marbels, 8 white marbles and 4 green marbles,

Question:

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

(i) red?

(ii) white?

(iii) not green?

Solution:

GIVEN: A box contains 5 red, 4 green and 8 white marbles and a marble is drawn at random

TO FIND: Probability of getting a marble

(i) red

(ii) white

(iii) not green

Total number of marble: 

(i) Total number red marble are 5

We know that PROBABILITY = 

Hence probability of getting red marble 

(ii) Total number of white marbles are 8

We know that PROBABILITY = 

Hence probability of getting white marble is 

(iii) Total number of green marbles is 4

We know that PROBABILITY = 

Hence probability of getting green marbles 

We know that sum of probability of occurrence of an event and probability of non occurrence of an event is 1.

$P(E)+P(\bar{E})=1$

$\frac{4}{17}+P(\bar{E})=1$

$P(\bar{E})=1-\frac{4}{17}$

$P(\bar{E})=\frac{17-4}{27}=\frac{13}{17}$

Hence the probability of getting green marbles is $P(\bar{E})=\frac{13}{17}$

 

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