A 1010-sided die is rolled. the die's faces are labeled with the numbers 1 through 1010, and each number is equally likely to
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<h2><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>:-</h2>
What is the value of this expression when c = -4 and d = 10 ? (c³ + d²)
(c³ + d²) where c = -4 and d = 10
The value of the expression (c³ + d²)
(c³ + d²) [Given expression]
Now, putting the value of c = -4 and d = 10 , we get,
{ (-4)³ + (10)² }
( -64 + 100 )
( 36 )
× 36
Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the <em>binomial distribution</em> is used to solve this question.
Binomial probability distribution
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.
In this problem:
- There are 9 rolls, hence
.
- Of the six sides, 2 are 3 or 4, hence
The desired probability is:
In which:
Then
Then:
0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For more on the binomial distribution, you can check brainly.com/question/24863377