# Calculate Probability of Successfully Rolling 5 Times

• MHB
• Agvantentua
In summary, the individual is seeking help understanding the correct method for calculating their probability of hitting the correct roll at least once in five tries. They have a 70% chance of the roll happening and a 1/14 chance of it being the right result. The suggested method is to calculate the probability of no success in five rolls and subtract that from 1 to find the probability of at least one success.
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.

Agvantentua said:
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.

## 1. What is the formula for calculating probability?

The formula for calculating probability is the number of desired outcomes divided by the total number of possible outcomes.

## 2. How do you determine the number of desired outcomes?

The number of desired outcomes can be determined by counting the number of outcomes that meet the given criteria. For example, if we want to calculate the probability of rolling a 6 on a standard die, the number of desired outcomes would be 1 (since there is only one side with a 6).

## 3. What is the total number of possible outcomes when rolling a die 5 times?

The total number of possible outcomes when rolling a die 5 times is 6^5 = 7776. This is because there are 6 possible outcomes for each of the 5 rolls.

## 4. How do you use the formula to calculate the probability of successfully rolling 5 times?

To calculate the probability of successfully rolling 5 times, we would first determine the number of desired outcomes (i.e. the number of times we want to roll a specific number). Then, we would divide that number by the total number of possible outcomes (i.e. 7776). The resulting number would be the probability of successfully rolling 5 times.

## 5. Can the probability of successfully rolling 5 times be greater than 1?

No, the probability of successfully rolling 5 times cannot be greater than 1. This is because the probability is a measure of the likelihood of an event occurring, and it cannot exceed 100% (or 1 in decimal form).

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