If an event has a 55% chance of

matt roberts

matt roberts

Answered question

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?

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-23Added 184 answers

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 1p.
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:
P({exactly 2 successes in 4 trials})=(42)·p2·(1p)42
Substituting the values, we have:
P({exactly 2 successes in 4 trials})=(42)·0.552·(10.55)42
Calculating the numerical value, we find:
P({exactly 2 successes in 4 trials})0.3562
2. The event happens exactly three times in 4 trials:
Using the binomial probability formula again, we have:
P({exactly 3 successes in 4 trials})=(43)·p3·(1p)43
Substituting the values, we get:
P({exactly 3 successes in 4 trials})=(43)·0.553·(10.55)43
Calculating the numerical value, we find:
P({exactly 3 successes in 4 trials})0.2907
3. The event happens all 4 times in 4 trials:
Again, using the binomial probability formula, we have:
P({exactly 4 successes in 4 trials})=(44)·p4·(1p)44
Substituting the values, we get:
P({exactly 4 successes in 4 trials})=(44)·0.554·(10.55)44
Calculating the numerical value, we find:
P({exactly 4 successes in 4 trials})0.0915
Now, to determine the chances of the event happening more than once in 4 trials, we sum up the probabilities of the three scenarios:
P({more than once in 4 trials})=P({exactly 2 successes in 4 trials})+P({exactly 3 successes in 4 trials})+P({exactly 4 successes in 4 trials})
Substituting the calculated values, we have:
P({more than once in 4 trials})0.3562+0.2907+0.0915
Calculating the numerical value, we find:
P({more than once in 4 trials})0.7384
Therefore, the chances of the event happening more than once in 4 trials is approximately 0.7384, or 73.84%.

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