Probability of getting one of colorful marbles

Ex1. Ajar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?
Solution:

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Ex2. A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be
(i) white? (ii) blue? (iii) red?
Solutions:
Saying that a marble is drawn at random is a short way of saying that all the marbles are equally likely to be drawn. Therefore, the number of possible outcomes =3+2+4=9 (Why?)
Let W denote the event ‘the marble is white’, B denote the event ‘the marble is blue’ and R denote the event ‘marble is red’.
(i) The number of outcomes favorable to the event n(W)=2
So, P(W)=2/9
Similarly, (ii) P(B)=3/9=⅓ and (iii) P(R)=4/9
Note that P(W)+P(B)+P(R)=1.

Ex3. 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?
Solutions:
Total number of marbles=5+8+4=17
(i) Number of red marbles=5
Probability of getting a red marble =5/17
(ii) Number of white marbles=8
Probability of getting a white marble=8/17
(iii) Number of green marbles=4
Probability of getting a green marble=4/17
Probability of getting a non green marble=1-4/17=13/17
It has got equal meaning of probability of getting either a green marble or a white marble.

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Ex4. A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is ⅔. Find the number of blue balls in the jar.
solution:
Total number of marbles =24
Let the total number of green marbles be x.
Then, total number of blue marbles =24-x
P(getting a given marble)=x/24
According to the condition given in the question,
x/24=⅔

Therefore, total number of green marbles in the jar =16. Hence, total number of blue marbles =24-x=24-16=8.

Ex5. The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is ¼. The probability of selecting a white marble at random from the same jar is ⅓. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?
Solution:
Let the number of green marbles =x
The number of white marbles =y
Number of yellow marbles =10
Total number of possible outcomes =x+y+10 (total number of marbles)

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Total number of marbles in jar =x+y+10=6+8+10=24

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