9.1 Probability of an Event


9.1 Probability of an Event
The probability of an event A, P(A) is given by

P ( A ) = Number of times event A occurs Number of trials P ( A ) = n ( A ) n ( S ) where 0 ≤ P ( A ) ≤ 1  

If P(A) = 0, then the event A will certainly not occur.
If P(A) = 1, then the event A is sure to occur.


Example 1:
A box contains 9 red pens and 13 blue pens. Tom puts another 4 red pens and 2 blue pens into the box. A pen is picked at random from the box. What is the probability that a red pen is picked?

Solution:
n(S) = 9 + 13 + 4 + 2 = 28
Let A = Event that a red pen is picked
n(A) = 9 + 4 = 13
P ( A ) = n ( A ) n ( S ) = 13 28


Example 2:
A bag contains 45 green cards and yellow cards. A card is picked at random from the bag. The probability that a green card is picked is 1 5 .  How many green cards must be added to the bag so that the probability of picking a green card becomes ½?

Solution:
n(S) = 45
Let
x = number of green cards in the bag.
A = Event of randomly picking a green card.
n(A) = x
P ( A ) = n ( A ) n ( S ) 1 5 = x 45 x = 45 5 x = 9

Let y is the number of green cards added to the bag.
9 + y 45 + y = 1 2
2 (9 + y) = 45 + y
 18 + 2y= 45 + y
2y – y = 45 – 18
y = 27

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