if E and F are independent events, find P(F) if P(E)=0.2 and P(E U F)= 0.3

Question

if E and F are independent events, find P(F) if P(E)=0.2 and P(E U F)= 0.3

Answer 1

Let P(F)= X

since E and F are independent eveents,
P(EnF)= P(E)* P(F)
therefore, P(EnF)= 0.2X
but P(EuF)=P(E)+ P(F)- P(EnF)
0.3= 0.2 + x - 0.2x
x = 1/8

Answer 2

Independent does not mean mutually exclusive, thus

P(EUF)=P(E)+P(F)-P(EnF)

Independence allows us to write:

P(EUF)=P(E)+P(F)-P(E)P(F)
P(EUF)=P(E)+[1-P(E)]P(F)

Therefore,

P(F)= [P(EUF)-P(E)]/[1-P(E)]

P(F)=[0.3-0.2]/[1-0.2]
=.1/.8
=1/8

Answer 3

Well, let's clown around with these probabilities! Since E and F are independent events, we know that the probability of both of them occurring together (E ∩ F) is equal to the product of their individual probabilities.

Now, we are given that P(E U F) = 0.3, which represents the probability that either E or F or both occur. Since E and F are independent, their intersection will be empty (E ∩ F = Ø), and the probability of E union F can be written as:

P(E U F) = P(E) + P(F) - P(E ∩ F)

Since E and F are independent, P(E ∩ F) = 0, which simplifies the equation to:

0.3 = 0.2 + P(F) - 0

We can rearrange the equation to solve for P(F):

0.3 - 0.2 = P(F)

Finally, we end up with the answer:

P(F) = 0.1

So, the probability of event F is 0.1. Keep on clowning around with those probabilities!

Answer 4

To find the probability of event F, given that events E and F are independent, we can use the formula:

P(E U F) = P(E) + P(F) - P(E ∩ F)

Given that P(E) = 0.2 and P(E U F) = 0.3, we can rearrange the formula to solve for P(F):

0.3 = 0.2 + P(F) - P(E ∩ F)

Since E and F are independent events, the probability of their intersection, P(E ∩ F), is equal to the product of their individual probabilities:

P(E ∩ F) = P(E) * P(F)

We substitute this into the equation:

0.3 = 0.2 + P(F) - (0.2 * P(F))

Now, we can solve for P(F):

0.3 = 0.2 + P(F) - 0.2P(F)

Combining like terms:

0.3 = 0.2 + (1 - 0.2)P(F)
0.3 = 0.2 + 0.8P(F)

We isolate P(F) by subtracting 0.2 from both sides:

0.1 = 0.8P(F)

Finally, we divide both sides by 0.8 to solve for P(F):

P(F) = 0.1 / 0.8
P(F) = 0.125

Therefore, the probability of event F, given that events E and F are independent, is 0.125 or 12.5%.

Answer 5

sorry, i made a mistake, for mutually exculsive events, P(EnF)= 0, hence,

from the previous equation,
0.3=0.2+P(F)-0
so P(F)= 0.1

Answer 6

If F and E are independent events then P(E and F) = 0

and we also know
P(E or F) = P(E) + P(F) - P(E and F)
.3 = .2 + P(F) - 0
P(F) = .1