What is the probability of one or both events occurring.

September 18, 2009 12:55 PM

What is the probability of one or both events occurring.

Seems like this should be a simple problem. but I have been unable to figure it out. Any help in the form of an answer or a pointer to somewhere that would help me solve it would be very nice.

A procedure is about to occur. There is a 1/100 chance that outcome X will occur, and a 1/200 chance that Y will occur. The outcomes are independent of each other. What is the probability that one or both of the outcomes will occur?

posted by charlesminus to science & nature (5 comments total)

1/100 + (99/100 * 1/200)
posted by 256 at 12:58 PM on September 18

What is the probability that one or both of the outcomes will occur?

1 minus the probability that neither event will occur. so 1 - (99/100)*(199/200) = .01495 ~ 1.5%

Disclaimer: It's been awhile since I took a probability class.
posted by muddgirl at 12:58 PM on September 18 [3 favorites]

Joint probability for independent events is P(X)*P(Y)

So the probability that both X and Y will happen ( P(X and Y) ) is:

1/100 * 1/200 = 1/20000

Probability for at least one of the events to occur is P(X) + P(Y) - P(X)*P(Y)

So the probability that either X or Y will happen ( P(X or Y) ) is:

1/100 + 1/200 - 1/20000 = 0.01495, which is around 1/67


Wikipedia can get you started with this kind of stuff.
posted by demiurge at 1:06 PM on September 18 [1 favorite]

(1/100)*(199/200) + (1/200)*(99/100) + (1/200)*(1/100) = 0.00995 + 0.00495 + 0.00005 = 1.495% chance

Easier way of doing this is to consider that the only way for your condition to NOT be true is if neither event happens. So (99/100) * (199/200) = 0.98505. This is the chance that your condition of one or both events happening will NOT be true. So the rest is the chance that your condition will be true. Thus, 1 - 0.98505 = 0.01495 = 1.495%
posted by fourmajor at 2:45 PM on September 18

Great, thank you so much. I will study and, I hope, understand.
posted by charlesminus at 4:42 PM on September 18