Find P(C|Y) from the information in the table. To the nearest tenth, P(C|Y) = .

	X	Y	Z	Total
A	32	10	28	70
B	6	5	25	36
C	18	15	7	40
Total	56	30	60	146

Solution:

Given,

P(C|Y) = ?

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.

Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

P(C|Y) reads the probability of event C happening given event Y is happening.

This is a conditional probability and the formula is given as

P(C|Y) = P(C ∩ Y)/ P(Y)

From the table,

P(C ∩ Y) = 15/146

P(Y) = 30/146

P(C|Y) = P(C ∩ Y)/ P(Y)

P(C|Y) = 15/146 / 30/146

P(C|Y) = 15/30

P(C|Y) = 0.5

Therefore, P(C|Y) = 0.5

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Find P(C|Y) from the information in the table. To the nearest tenth, P(C|Y) = .

Summary:

P(C|Y) from the information in the table is 0.5