SOLUTION: For two events, E and F, you are given: P(E) = 0.30 P(F) = 0.45 E and F are mutually exclusive events What is the value of P(F | E)? Enter your answer as a decimal rounded t

Algebra.Com
Question 1196908: For two events, E and F, you are given:
P(E) = 0.30
P(F) = 0.45
E and F are mutually exclusive events
What is the value of P(F | E)? Enter your answer as a decimal rounded to two decimal places.

Found 2 solutions by math_helper, math_tutor2020:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
E and F are mutually exclusive. Thus, on one trial/sample, if one event happens then the other can not happen.
Think of flipping a coin once, if you get heads then you can not get tails.
For the given problem, this means P(F|E) = 0 (0.00)

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The vertical bar means the keyword "given"

P(F | E) = P(F given E)

Mutually exclusive events are two events that have no overlap, and cannot happen simultaneously
Because E and F are mutually exclusive, this means
P(E and F) = 0
aka
P(F and E) = 0

Then we can use the conditional probability formula
P(F given E) = P(F and E)/P(E)
P(F given E) = 0/(0.30)
P(F given E) = 0

If event E happens, then we know that event F cannot happen (since they cant happen simultaneously)
Therefore, we know P(F) is zero if we know E happened already

RELATED QUESTIONS

For two events, E and F, you are given: P(E) = 0.30 P(F) = 0.45 E and F are mutually (answered by ikleyn)
E and F are mutually exclusive events. P(E) = 0.15; P(F) = 0.71. Find P(E | F) (answered by ikleyn)
Given that E and F are mutually exclusive events with the P(E) = 0.3 and the P(F) = 0.6,... (answered by stanbon)
E and F are mutually exclusive events. P(E) = 0.15; P(F) = 0.71. Find P(E | F) (answered by greenestamps,Edwin McCravy)
Suppose that E and F are two events and that P(E)=0.4 and P(F|E)=0.5. What is P(E and... (answered by MathLover1)
Supppse that E and F are two events and that P(E) = 0.28 and P(F|E) = 0.7 What is P(E and (answered by ikleyn)
Two events, E and F, are such that P(E)=2/5, P(F)=1/6 and P(E U F)=13/30. Show that E and (answered by Fombitz)
You are given the following: P(A)=0.25 P(B)=0.30 P(C)=0.55 P(A and C)=0.05 P(B and (answered by Edwin McCravy)
You are given the probabilities below: P(a) = 0.25 P(B) = 0.30 P(C) = 0.55 P(A and C) (answered by robertb,jim_thompson5910)