Given the list of probabilities, choose all of the correct statement. P (A) = 0.25 P (B) = 0.15 P (C) = 0.30 P (D) = 0.20 If the P (A and B) = 0.075, then events A and B are independent. If the P (A and C) = 0.15, then events A and C are independent. If the P (B and C) = 0.045, then events B and C are independent. If the P (C and D) = 0.06, then events C and D are independent.

Choose the last two statements as the correct ones

Step-by-step explanation:

In probabilities it is said that two events A and B are independent if the result of occurrence A does not affect the occurrence of B.

For this type of events it is established that:

If A and B are independent events, then:

P (A and B) = P (A) * P (B)

In this problem the probability of A, B, C and D occurs.

Then calculate P (A and B) as P (A) * P (B), if the result gives the same as in the statement of the problem, then it is true that A and B are independent, the same for the other combinations.

It is said that P (B and C) = 0.045

Then let's do:

P (B and C) = P (B) * P (C) = 0.15 * 0.30 = 0.045

It is fulfilled, then B and C are independent.

You can check that the same happens for P (C and D) = 0.06

P (C and D) = P (C) * P (D) = 0.30 * 0.20. = 0.06.

So the statement is correct, C and D are independent.

The first two statements are not fulfilled.

Finally choose the last two statements as the correct ones