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Find P(Y|B) from the information in the table.

A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 8, 6, 23, 37. The third column is labeled Y with entries 80, 34, 56, 170. The fourth column is labeled Z with entries 40, 45, 32, 117. The fifth column is labeled Total with entries 128, 85, 111, 324.

To the nearest tenth, what is the value of P(Y|B)?

0.2
0.3
0.4
0.5

Answer :

SaniShahbaz

Answer:

0.4

Step-by-step explanation:

The table with correct formatting is attached in the image below.

We have to find P(Y | B). This is a conditional probability i.e. probability of Y given B.

The formula of conditional probability for two event A and B is:

[tex]P(A|B)=\frac{P(A \cap B)}{P(B)}[/tex]

So, for the given case, the formula would be:

[tex]P(Y|B)=\frac{P(Y \cap B)}{P(B)}[/tex]

P(Y ∩ B) indicates the probability of Y and B occurring together. Y and B occur together 34 times out of total of 324, so:

[tex]P(Y \cap B)=\frac{34}{324}[/tex]

P(B) indicates the probability of occurrence of B. B occurs 85 times in a total of 324. So,

[tex]P(B)=\frac{85}{324}[/tex]

Using these values in the formula of conditional probability, we get:

[tex]P(Y \cap B)=\frac{\frac{34}{324}}{\frac{85}{324} }\\\\ =\frac{34}{85}\\\\ =0.4[/tex]

Thus, the value of P(Y|B) is 0.4

twisztedbombshell

Answer:

C. 0.4

Step-by-step explanation:

correct on edge, have a nice day:)

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