Adding or multiplying likelihood of passing

Question

In some cases I see probabilities being multiplied (for eg let's say to clear round 1 there is a 30% chance and to clear round 2 there is a 20% chance. The likelihood of clearing both rounds should be 30% x 20% = 60% or 30% + 20% = 50%? In some problems I see likelihood's being multiplied and in others I see it being added. So which one is it? When do we use one over the other?

Answer 1

Hi there,

For the example you reported, the probability to pass both rounds is the product of the two:

30%*20% = 6%

Whenever you want to find the probability to be successful in two independent situations, you should multiply the two probabilities.

Best,

Francesco

Answer 2

in general: If you have “or” in the wording, add the probabilities. If you have “and” in the wording, multiply the probabilities.

in your example it would be not possible to add, since you cannot pass R1 or pass R2

Answer 3

Anonymous B is spot on! :)

Answer 4

Hi there,

Unfortunately you're wrong on both calculations. You need to multiply the probabilities...30% x 20% is NOT 60%. It's 6%. (Remember the 0s).

So, if you're starting out in the process, your odds are 6%. But, if you're already at stage 2, then the odds now become 20%.

Please please learn proabilities...this concerns me in regards to your future casing. (Especially that you thought 30% x 20% was 60%).

Answer 5

Hi there,

To add to what others already said, I would also suggest to stop thinking of it as probabilities and use common sense to understand the problem:
Let's take your example:

Is it easier to pass two rounds than one? No. So I have less chance to pass two rounds than one. That already means that your probability can't be higher than 30% (prob to pass one round).

To pass two rounds I need to Pass one round and THEN to pass the second round hence why you multiply the two probability. Because the probability of the second event depends on the first one.

Now if I have independant event: I have interview with two firms what are the different probability? And you have 30% to pass any interview.
So you have four scenario:

Fail both interview
Pass with FIrm A and Fail with Firm B
Fail A and pass B
Pass A and B

To fail both interviews you must: fail interview A (70% chance) and THEN fail interview B (70% again)=> Probability for the event 70%*70%=49%

To pass both interview it's similar except i have 30% of success so the probability is 30%*30%=9%

Finally to pass A and fail B (or the opposite) the probability is 70%*30%=21%

Now what is the probability to pass 1 interview out of two?

Well I can EITHER fail A and pass B or pass A and fail B. Since those two events are unrelated (hence the either) the two probabilities are summed so 21%+21%=42%. And this is logical: after all it's easier to pass one interview (regardless of which one) than specifically succeeding interview A. Hence a higher probability.

Hope it helps