slickgreen323
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\use the Venn diagram to calculate probabilities.


Which probabilities are correct? Check all that apply.

P(A|C) = 2/3
P(C|B) = 8/27
P(A) = 31/59
P(C) = 3/7
P(B|A) = 13/27

use the Venn diagram to calculate probabilities Which probabilities are correct Check all that apply PAC 23 PCB 827 PA 3159 PC 37 PBA 1327 class=

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MrEquation
Answer: The first and the third.

The two statements that are correct are the first and third options. 

In the first choice, we are looking for values that are in A given that they are already a part of B. 14 of the values in B are also in A. This can be reduced to 2/3 as shown.

In the third choice, we are simply looking for the fraction of the entire chart that are in A. There are 31 values in A and 59 in the total chart. Therefore, the fraction 31/59 is correct.
JeanaShupp

Answer : 1 and 3 are the correct probabilities.

→According to the given Venn diagram.

Total number of elements  = 59.


1)P(C)=[tex]\frac{21}{59}[/tex] and [tex]P(A\cap C)=\frac{14}{59}[/tex] then

[tex]P(A|C)=\frac{P(A\cap C)}{P(C)}[/tex][tex]=\frac{\frac{14}{59}}{\frac{21}{59}}=\frac{14}{21}=\frac{2}{3}[/tex]

2)P(B)=[tex]\frac{27}{59}[/tex] and  [tex]P(C\cap B)=\frac{11}{59}[/tex] then

[tex]P(C|B)=\frac{P(C\cap B)}{P(B)}[/tex][tex]=\frac{\frac{11}{59}}{\frac{27}{59}}=\frac{11}{27}[/tex][tex]\neq \frac{8}{27}[/tex]

3) P(A) =[tex]\frac{number\ of\ elements\ in\ A}{Total\ elements}=\frac{31}{59}[/tex]

4) P(C) =[tex]\frac{number\ of\ elements\ in\ C}{Total\ elements}=\frac{21}{59}[/tex][tex]\neq \frac{3}{7}[/tex]

5) [tex]P(B|A)=\frac{P(B\cap A)}{P(A)}[/tex][tex]=\frac{\frac{13}{59}}{\frac{31}{59}}=\frac{13}{31}[/tex][tex]\neq \frac{13}{27}[/tex]

Therefore, option 1 and 3 are correct.

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