# Success Rate of an Event with 20% Chance & 5 Tries

• Zinic
In summary, the probability of success for an event with a 20% success rate and 5 chances is approximately 67%. This can be found by subtracting the probability of all 5 trials being failures (32.768%) from 1. To find this probability, the binomial distribution can be used, with the formula 1-(n-1/n)^n, which simplifies to 1-e^-1 (approximately 0.63) in the limit as n gets large. Alternatively, the probability of not succeeding can be found by multiplying the individual probabilities (4/5)^5, and then subtracted from 1 to find the probability of at least one success.
Zinic
Alright. I need to know what is the probability of something turning out successful if there are 5 chances for a certain event that has 20% success rate will occur.

If you don't understand what I am saying, I will try to reword it below.

If an event has a 20% chance of happening, and I only get 5 tries, what is the success rate for the event to happen overall?

Please explain how you came up with the solution. I will understand complicated work, so need to baby feed the walk though. Thank you very much.

Here's a hint: See if you can figure out the probability of not succeeding.

I tired thinking of solving this using a simplier problem. Such as flipping a coin 2 times and landing on heads. What are the chances of that.

I simple problem like this, and I still don't know what the chances of that happening

Thinking of not succeeding? Hmm. 80% chance of not happening successful. I don't see how that would help.

Look at your coin toss problem, to see how that may be helpful.

If you toss a coin twice, what are the possible outcomes? List them. How many of these cases contains a success (at least one H)? How many are failures (no H)? So what is the probability of failure from 2 coin tosses?

Zinic said:
80% chance of not happening successful.
80% chance of failure for a single try. What's the chance of failing on all 5 tries?

Gokul43201 said:
Look at your coin toss problem, to see how that may be helpful.

If you toss a coin twice, what are the possible outcomes? List them. How many of these cases contains a success (at least one H)? How many are failures (no H)? So what is the probability of failure from 2 coin tosses?

There are two, 50% chances of it landing on heads. Same with tails. So is it for 2 coin tosses. The chances for not landing on head in 50%? So 50% of it landing on heads. Right?

Doc Al said:
80% chance of failure for a single try. What's the chance of failing on all 5 tries?

Well, don't you multiply all the chances by the number of tries you get.

(4/5)^5 = .32768. 32.768% chance of failure.

Edit: wow, so the chance of success is 1 - .32768 = .67232 which is 67% success! Now I get it.

Last edited:
Let the r.v. X be the amount of successes from n trials of an experiment that is a success with probability p. Then X ~ Binomial(n,p). Look up the binomial distribution on wikipedia, for the pgf, and the moments. You need to find the "expected value" of this distribution, E(X), the first moment.

Interesting enough, this matter does not change much as n gets large. In the case of 10 tries with success rate of 1/10, the rate becomes .65. In the case of 1% chance and 100 tries = .63.

In fact, in the limit, to do the math: $$1-(\frac{n-1}{n})^n$$ = 1-e^(-1) = .63

ToxicBug said:
Let the r.v. X be the amount of successes from n trials of an experiment that is a success with probability p. Then X ~ Binomial(n,p). Look up the binomial distribution on wikipedia, for the pgf, and the moments. You need to find the "expected value" of this distribution, E(X), the first moment.

No, he does not need the expected value; that was not asked. Nor does he need the full binomial distribution. As almost everyone has been saying he simply needs to find the probability NONE of the 5 trials is a success, then subtract from 1 to find the probability that at least one trial is a success.

HallsofIvy said:
No, he does not need the expected value; that was not asked. Nor does he need the full binomial distribution. As almost everyone has been saying he simply needs to find the probability NONE of the 5 trials is a success, then subtract from 1 to find the probability that at least one trial is a success.
Yeah, you're right, I didn't understand the question and this morning I thought about exactly the same thing that you're saying :)

## 1. What is the probability of success for an event with a 20% chance and 5 tries?

The probability of success for an event with a 20% chance and 5 tries is approximately 67.2%. This can be calculated by using the binomial probability formula, where the number of trials (n) is equal to 5, the probability of success (p) is 0.2, and the number of successes (x) is greater than or equal to 1.

## 2. How does the success rate change if the number of tries is increased?

The success rate will increase as the number of tries increases. This is because with more tries, there are more opportunities for the event to occur. For example, if the number of tries is increased to 10, the success rate would be approximately 87.7%.

## 3. Is the success rate affected by the initial chance of the event?

Yes, the initial chance of the event does affect the success rate. In this case, a 20% chance results in a higher success rate compared to a 10% or 5% chance. However, the effect of the initial chance decreases as the number of tries increases.

## 4. Can the success rate be higher than 100%?

No, the success rate cannot be higher than 100%. This is because the success rate is a measure of the likelihood of an event occurring, and a probability cannot exceed 1 or 100%.

## 5. How can we improve the success rate of an event with a 20% chance and 5 tries?

The success rate can be improved by increasing the number of tries or increasing the initial chance of the event. Additionally, using strategies such as trial and error or adjusting the approach to the event may also increase the probability of success.

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