If events E and F are independent and each has probability p of

Question

If events  E  and  F  are independent and each has a probability  p  of occurring, which of the following represents the probability that  E  will occur but  F  will not occur?

A) p^2
B) 1-p^2
C) p^2-1
D) p^2-p
E) p-p^2

gmatophobia · Accepted Answer

Event E

Probability of occurring = p 
 Probability of  not   occuring = 1-p

Event F

Probability of occurring = p 
 Probability of  not   occuring = 1-p

Required Probability = P(Event E occurring) * P(Event F not occurring)

= p * (1-p)

= p - p^2

Option E

JeffTargetTestPrep · Answer

If events E and F are independent, then E and not-F are independent as well. (Also, not-E and F are independent, and not-E and not-F are independent.)

P(E and not-F) = P(E) × P(not-F) = p × (1 – p) = p – p^2

Answer: E

ramiav · Answer

I solved that in another way:

Probability of both p^2
Probability of no E and no F (1-p)^2
as p is equal on both cases

All - both - neither
---------------
2

(1 - (1-p)^2 - p^2)/2 = 2(p-p^2)/2

MalachiKeti · Answer

Why it cant be D p^2-p  Bunuel

Bunuel · Answer

How are you getting p^2 - p? What’s your reasoning behind it? I think if you think it through carefully, you’ll spot the flaw in your reasoning yourself.

reighlyschultz · Answer

This problem was easier for me to plug and check. You would want to pick an easy number to understand, so in this case, let's say each event has a 10% or 1/10 chance of happening.

That means that odds of the event described will be (1/10)*(9/10) which is 9/100. Now we plug and go

(1*10)^2 Nope
1-(1*10)^2 Nope
ETC 
Until E
(1/10)-(1/10)^2

(1/10)-(1/100)

(10/100)-(1/100)= 9/100

Answer Choice E

DrHetal · Answer

Probability of occurance of event = p , so probability of event not occuring is 1-p
P(E Occur) and P (F not occur)=
p (1-p) 
p-p^2

bumpbot · Answer

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If events E and F are independent and each has probability p of

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If events E and F are independent and each has probability p of

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