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:
https://brainly.com/question/25870256
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