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Answer:
0.2992 = 29.92% probability of obtaining at least 8 failures.
Step-by-step explanation:
For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
A success is 5 or 6.
A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:
10 normal six sided dice are thrown.
This means that
Find the probability of obtaining at least 8 failures.
This is:
So
Then
0.2992 = 29.92% probability of obtaining at least 8 failures.