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1 answer:
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Answer:
- 4
- 25
Step-by-step explanation:
A calculator is your friend for such problems.
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Evaluating these by hand, the <em>Order of Operations</em> applies. First you do what's in parentheses, then you do multiplication, then addition/subtraction.
1. (3/4)·(12·4 -16) -20 = (3/4)(48 -16) -20 = (3/4)·32 -20 = 24 -20 = 4
2. (5/9)·(12·6 -42 +15) = (5/9)·(72 -42 +15) = (5/9)·(30 +15) = (5/9)·45 = 25
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Of course, the <em>Order of Operations</em> applies within each level of parentheses.
Adding the opposite of a number is the same as subtraction. Likewise, subtracting the opposite of a number is the same as adding the number. The usual associative and commutative properties of addition and multiplication apply. Among other things, that means you can compute the product of an integer and a fraction in any convenient way:
(3/4)·32 = 3·(32/4) = 3·8 = 24
(5/9)·45 = 5·(45/9) = 5·5 = 25
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