A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 45, 20, 25, 90. The third column is labeled Y with entries 30, 10, 35, 75. The fourth column is labeled Z with entries 60, 25, 50, 135. The fifth column is labeled Total with entries 135, 55 110, 300. 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).

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rishipatel252 rishipatel252 · Answer 1 · 2020-04-06T17:31:00+02:00

Answer:

Step-by-step explanation:

To see if two events are independent you can use the formula P(a|b) = P(a)

In this problem P(C|Y) = 35/75 = .4667 and P(C) = 110/300 = 3.667,

therefore C and Y are not independent events because P(C∣Y) ≠ P(C).

The answer is choice D

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MrRoyal MrRoyal · Answer 2 · 2022-05-10T11:42:55+02:00

The true statement about events C and Y is (d) C and Y are not independent events because P(C∣Y) ≠ P(Y).

The events C and Y are dependent if the following equation is true:

P(C∣Y) = P(C)

From the table, we have the following parameters:

n(C) = 110

n(C and Y) = 35

n(Y) = 75

Total = 300

So, we have:

P(C) = n(C)/Total

This gives

P(C) = 110/300

P(C) = 0.367

Also, we have:

P(C|Y) = P(C and Y)/P(Y)

This gives

P(C|Y) = 35/75

P(C|Y) = 0.467

By comparison. P(C∣Y) ≠ P(C).

Hence, the true statement about events C and Y is (d) C and Y are not independent events because P(C∣Y) ≠ P(Y).