How Likely Is More Than Two Successes in Six Trials with 10% Success Rate?

[nachelle]

given trails n = 6, success probability p = 0.1

$$P(x > 2) = 1 - P(x \leq 2)$$
$$P(x \leq 2) = \left( \begin{array}{c} 8 \\ 0 \end{array} \right) 0.3^0 (1-0.3)^{8-0} + \cdots$$ (sum until x = 2, including that case)

help

 

[radou]

First, do not post same questions. Second, if you expect someone to solve the whole problem step by step (i.e. number by number), then you might be in the wrong forum. Third, without using your head, you won't solve any problem. Fourth, I'm not being rude.

 

[Architeuthis Dux]

please

[/QUOTE]

Sure, I can help you with this probability problem. It seems like you are trying to find the probability of having more than 2 successes out of 6 trials, given a success probability of 0.1. First, let's clarify some notation:

- n = 6 represents the number of trials
- p = 0.1 represents the probability of success for each trial
- P(x > 2) represents the probability of having more than 2 successes out of 6 trials

To solve this problem, we can use the binomial distribution formula, which is P(x) = (n choose x) * p^x * (1-p)^(n-x). Using this formula, we can calculate the probability of having exactly 0, 1, or 2 successes out of 6 trials. Then, we can subtract this probability from 1 to get the probability of having more than 2 successes.

So, let's start by finding the probability of having exactly 0, 1, or 2 successes out of 6 trials:

- P(x = 0) = (6 choose 0) * 0.1^0 * (1-0.1)^(6-0) = 0.5314
- P(x = 1) = (6 choose 1) * 0.1^1 * (1-0.1)^(6-1) = 0.3543
- P(x = 2) = (6 choose 2) * 0.1^2 * (1-0.1)^(6-2) = 0.0984

Now, we can add these probabilities together to find the total probability of having 0, 1, or 2 successes:

P(x \leq 2) = 0.5314 + 0.3543 + 0.0984 = 0.9841

Finally, we can subtract this probability from 1 to find the probability of having more than 2 successes:

P(x > 2) = 1 - P(x \leq 2) = 1 - 0.9841 = 0.0159

Therefore, the probability of having more than 2 successes out of 6 trials, given a success probability of 0.1, is approximately 0.0159 or 1.59