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Probability: Examples
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Probability
Probability is the likelihood or chance of an event occurring.

Probability = the number of way's of achieving success / the total number of possible outcomes

Example: A bag contains 5 blue balls, 8 red balls, 4 green balls and 7 yellow balls. If one ball is drawn at random, find the probability that it is
(i) yellow
(ii) blue
(iii) not green.
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Solution: Total number of balls in the bag = 5 + 8 + 4 + 7 = 24.
Total number of elementary events = 24.

(i) There are 7 yellow balls in the bag.
Favorable number of elementary events = 7
Hence, P (Getting a yellow ball) = -7/24.

(ii) There are 5 blue balls in the bag.
Favorable number of elementary events = 5
Hence, P (Getting a blue ball) = 5/24.

(iii) There are 5 + 8 + 7 = 20 balls which are not green.
Favorable number of elementary events = 20
Hence, P (Not getting a green ball) = 20/24 = 5/6.

Probability
Example: A bag contains 7 red balls and some black balls. If the probability of drawing a black ball is doubles that of a red ball, find the number of black balls in the bag.
Solution: Let there be x black balls in the bag 
Total number of balls in the bag = (7 + x)
Now,
p1 = Probability of drawing a black ball = x / (7 + x)
p1 = Probability of drawing a red ball = 7 / (7 + x)
It is given that p1 = 2p1
x / (7 + x) = 2 * 7 / (7 + x
x / (7 + x) = 14 / (7 + x
x = 14
Hence, there are 14 black balls in the bag.
 
   
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