Total number of possible results of rolling 2 dice = 6 x 6 = 36
Total number of ways they can both show the same face = 6
Probability of showing the same face = 6/36 = <u>1/6</u> = 16 and 2/3 percent.
Using the binomial distribution, it is found that there is a 0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
<h3>What is the binomial distribution formula?</h3>
The formula is:


The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
With 5 shoots, the probability of making at least one is
, hence the probability of making none, P(X = 0), is
, hence:

![\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B%281%20-%20p%29%5E5%7D%20%3D%20%5Csqrt%5B5%5D%7B%5Cfrac%7B232%7D%7B243%7D%7D)
1 - p = 0.9908
p = 0.0092
Then, with 6 shoots, the parameters are:
n = 6, p = 0.0092.
The probability that at least two of them make it inside the recycling bin is:

In which:
[P(X < 2) = P(X = 0) + P(X = 1)
Then:



Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.9461 + 0.0527 = 0.9988

0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
More can be learned about the binomial distribution at brainly.com/question/24863377
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Answer:x=1/2
Step-by-step explanation:
Complete Question
A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?
Answer:
The 95% confidence interval is 
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
Step-by-step explanation:
From the question we are told that
The total sample size is 
The number of offspring that is yellow peas is 
The number of offspring that is green peas is
The sample proportion for offspring that are yellow peas is mathematically evaluated as

Given the the confidence level is 95% then the level of significance is mathematically represented as


The critical value of
from the normal distribution table is

Generally the margin of error is mathematically evaluated as

=> 
=> 
The 95% confidence interval is mathematically represented as

=> 
=> 
Answer:
5
Step-by-step explanation:
thanks for the points