Which statement is true about whether C and Y are independent events? C and Y are independent events because P(C∣Y) = P(Y). C and Y are independent events because P(C∣Y) = P(C). C and Y are not independent events because P(C∣Y) ≠ P(Y). C and Y are not independent events because P(C∣Y) ≠ P(C).

Found the complete problem, see attachment.

My answer:
C and Y are not independent events because P(C∣Y) ≠ P(C).

Probability of C = 110/300 = 0.37
Probability of Y = 75/300 = 0.25

Probability of (C|Y) = 0.37 * 0.25 = 0.0925

As you can see, P(C∣Y) is 0.0925 which is not equal to P(C) = 0.37. Thus, C and Y are not independent events.

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-02-20T15:00:52+01:00

Statement which is true about whether C and Y are independent events is "C and Y are not independent events because [tex]P(C|Y) \neq P(C).[/tex]"

What is the independent events?

Independent events are those events whose occurrences does not depends on the other events.

Given information-

In the given table,

The total numbers of outcome is 300.

The total number of times event C occur is 110.

The total number of times event Y occur is 75.

As the probability of an event is the ratio of favorable outcome to the total number outcome. Therefore the probability of the event C can be given as,

[tex]P(C)=\dfrac{110}{300} \\P(C)=\dfrac{11}{30}\\P(C)=0.37[/tex]

Thus the probability of the event C is 11/30. Now the probability of the event Y can be given as,

[tex]P(C)=\dfrac{75}{300} \\P(C)=0.25[/tex]

Thus the probability of the event Y is 11/30.The probability of P(C|Y) can be given as,

[tex]P(C|Y)=P(C)\times P(Y)\\P(C|Y)=0.37\times0.25\\P(C|Y)=0.0925[/tex]

As,

[tex]P(C|Y)\neq P(C)[/tex]

Hence, C and Y are not independent events because, [tex]P(C|Y) \neq P(C).[/tex]

Thus the option 4 is the correct option.

Learn more about the independent events here;

https://brainly.com/question/12700357