Solving Probability Questions: A, B, and C Events with Given Probabilities

[Questions999]

We have three events A B C and three probabilities P(A)=1/4 ,P(B)= 1/3 and P(C)=1/2
I have to find the probability a) that none of them happens...this is impossible in my opinion ,so the probability is zero
b)Find the probability that a certain event happens :this is P(A)+P(B)+P(C) because the probability in this case is A U B U C...but their sum is bigger than 1..so how do I do this one?

 

[CompuChip]

For a) - why is it impossible? The probability of each of the events is less than 50%, so my intuition tells me it is pretty likely that none of them happens. For example, if there is a 5% chance of snow tomorrow, 25% chance of thunderstorms and 50% chance of rain, would you say it is impossible that will be sunny and dry?

Instead of going by your opinion, let's try to do the math :) If P(A) = 1/4, what is the probability that P(not A)? If P(A) = 1/4 and P(B) = 1/3, what is the probability of both, i.e. P(A and B)?

 

[HallsofIvy]

We have three events A B C and three probabilities P(A)=1/4 ,P(B)= 1/3 and P(C)=1/2
I have to find the probability a) that none of them happens...this is impossible in my opinion ,so the probability is zero

What is that "opinion" based on? Notice that 1/4+ 1/3+ 1/2= 3/12+ 4/12+ 6/12= 13/12> 1. What does that tell about these events?

b)Find the probability that a certain event happens :this is P(A)+P(B)+P(C) because the probability in this case is A U B U C...but their sum is bigger than 1..so how do I do this one?

"A certain event" is ambiguous. It doesn't make sense for it to mean just "a specific event" because that event is not given. If it means "an event that is certain to happen" then the answer has nothing to do with A, B, or C. The probability of an event that is certain to happen is alway a specific number- what number is that?

 

[Questions999]

So,the first one,since the probability can't be bigger than one,the first one is impossible :)
The second one,the probability is 1.Am I right now? :)

 

[Ray Vickson]

So,the first one,since the probability can't be bigger than one,the first one is impossible :)
The second one,the probability is 1.Am I right now? :)

No. The first one is possible. It depends on details about A, B and C that you are not given. You can construct examples of A, B and C where the probability in (a) ranges from 0 to 50%.

The second question is too vaguely stated to make sense.