Find P(Y|B) from the information in the table. To the nearest tenth, what is the value of P(Y|B)?

	X	Y	Z	Total
A	8	80	40	128
B	6	34	45	85
C	23	56	32	111
Total	37	170	117	324

Solution:

Given,

P(Y|B) = ?

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(Y|B) reads probability of event Y happening given event B is happening.

This is a conditional probability and the formula is given as

P(Y|B) = P(Y ∩ B)/ P(B)

From the table,

P(Y ∩ B) = 34/324

P(B) = 85/324

P(Y|B) = (34/324) / (85/324)

P(Y|B) = 34/85

P(Y|B) = 0.4

Therefore, P(Y|B) = 0.4

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Find P(Y|B) from the information in the table. To the nearest tenth, what is the value of P(Y|B)?

Summary:

P(Y|B) from the information in the table is 0.4