Question

If P(En F) = 0.036, P(E|F) = 0.09, and P(F|E) = 0.1, then (a) P(E) = (b) P(F) = = (c) P(EUF) (d) Are the events E and Findependent? =​

Answer 1

The events E and F are not independent

How to determine the probabilities?

The given parameters are:

P(E n F) = 0.036

P(E|F) = 0.09

P(F|E) = 0.1

To calculate P(E), we use:

P(F|E) = P(E n F)/P(E)

This gives

P(E) = P(E n F)/P(F|E)

So, we have:

P(E) = 0.036/0.1

Evaluate

P(E) = 0.36

To calculate P(F), we use:

P(E|F) = P(E n F)/P(F)

This gives

P(F) = P(E n F)/P(E|F)

So, we have:

P(F) = 0.036/0.09

Evaluate

P(F) = 0.4

To calculate P(E U F), we use

P(E U F) = P(E) + P(F) - P(E n F)

So, we have:

P(E U F) = 0.36 + 0.4 - 0.036

Evaluate

P(E U F) = 0.724

The events E and F are independent if

P(E n F) = P(E) * P(F)

This gives

0.036 = 0.36 * 0.4

Evaluate

0.036 = 0.144 --- false

Hence, the events E and F are not independent

Read more about probabilities at:

brainly.com/question/25870256

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