Page 36 - Math SL HB Sem 3

Conditional Probability:

For two events that the occurrence of one would affect the likelihood of the occurrence of another
(E.9. selections without replacement), we are dealing with conditional probability.
Given event B has occurred, the probability that event./4 will occur is:
As restridion has been
P(A N B\ placed that event B
P(AIB) occurred first, itb P(B) in
P(B) the denominator

watch out:
P(AIB) + P(BIA)

\. Example:

A bag contains 3 white balls and 5 black balls. Amy selects one ball randomly from the bag and
draws another one without the replacement of the lirst.

1" selection 2'd selection
2
P(wlw) = WWW
1 G iven one white ball is taken
The original total Dunber oltt without replaceDenl
3 therc arc only 2 wllite balls
ofballs in the bag is W
3+5:B. I left in the bag and the total
Therc are 3 back balls oltt 5 B number of balls in the bag
ofB balls , so P(Blw) = wB'--... is 7. Hence,
1
5 P(w lw) = - 2
5 3
P(B) = P(wlB) = W BW
s 1
B

4
P(BIB) = - B BB

What is the probability that those two balls drawn are of the same colour?

\ sotution:

Watch Out:

Always look for'conditional probability' pointers - terms such as 'without replacement', ' given ...' , etc...

-b