matt roberts

2022-07-27

If an event has a 55% chance of happening in one trial, how do I determine the chances of it happening more than once in 4 trials?

Don Sumner

To determine the chances of an event happening more than once in 4 trials, we can use the concept of binomial probability.
In this case, we are given that the event has a 55% chance of happening in one trial. Let's denote the probability of success (event happening) as $p$, which is 55%, or $p=0.55$. The probability of failure (event not happening) is $1-p$.
To calculate the probability of an event happening more than once in 4 trials, we need to consider different scenarios:
1. The event happens exactly twice in 4 trials.
2. The event happens exactly three times in 4 trials.
3. The event happens all 4 times in 4 trials.
Let's calculate each scenario separately and then sum up the probabilities.
1. The event happens exactly twice in 4 trials:
To calculate this probability, we use the binomial probability formula:

Substituting the values, we have:

Calculating the numerical value, we find:

2. The event happens exactly three times in 4 trials:
Using the binomial probability formula again, we have:

Substituting the values, we get:

Calculating the numerical value, we find:

3. The event happens all 4 times in 4 trials:
Again, using the binomial probability formula, we have:

Substituting the values, we get:

Calculating the numerical value, we find:

Now, to determine the chances of the event happening more than once in 4 trials, we sum up the probabilities of the three scenarios:

Substituting the calculated values, we have:

Calculating the numerical value, we find:

Therefore, the chances of the event happening more than once in 4 trials is approximately 0.7384, or 73.84%.

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