Calculate Probability of Successfully Rolling 5 Times

[Agvantentua]

I'm sorry if it's the wrong forum. I'm just doing a project with little experience in probability, and it's really important for me that the method I use is correct, so I just preferred to ask someone that has some idea on the topic. If you were so kind to explain the method or at least tell me its name, I'd be very, very grateful.

Basically, I attempt to roll 5 times, and I have 70% chance for the roll to even happen. When roll happens I have 1/14 chance of rolling the right result. So what I'm looking for is simply my chance of hitting correct roll at least once in these 5 tries.I was trying to calculate that using binomal probability, but I'm not sure if that's the correct way.

 

[HallsofIvy]

I'm sorry if it's the wrong forum. I'm just doing a project with little experience in probability, and it's really important for me that the method I use is correct, so I just preferred to ask someone that has some idea on the topic. If you were so kind to explain the method or at least tell me its name, I'd be very, very grateful.

Basically, I attempt to roll 5 times, and I have 70% chance for the roll to even happen. When roll happens I have 1/14 chance of rolling the right result. So what I'm looking for is simply my chance of hitting correct roll at least once in these 5 tries.I was trying to calculate that using binomal probability, but I'm not sure if that's the correct way.

The probability of "at least once" is 1 minus the probability of "not at all" so start by calculating the probability of no success in 5 rolls. On anyone roll "failure" can happen in two ways- the roll can not happen at all or the roll can happen but not be a success.

The probability the roll does not happen is 0.3 and the probability it does happen is 0.7. If the roll does happen, the probability of "not getting the right result" is 0.75. The overall probability of "not getting the right result" on anyone roll is 0.3+ 0.7(0.75)= 0.825. The probability of that happening five times is $$0.825^5= 0.3822$$ (to four decimal places) so the probability of "at least one success" in five trials is 1- 0.3822= 0.6178.