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postnew [5]
3 years ago
7

Movie tickets are $8 for shows after 6 pm and $5.50 for shows before 6 pm. If 80 tickets are sold for a total of $575, which sys

tem of equations could be used to find the number of each type of ticket sold? *
1.x+y=8; 5.50x+80y=575
2.x+y=575; 5.50x+8y=80
3.x+y=80; 575x+8y=5.50
4.None of these
5.x+y=80; 5.50x+8y=575​
Mathematics
1 answer:
Dominik [7]3 years ago
5 0
The answer is 5. x+y=80; 5.50x+8y=575
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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

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

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In this problem:

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The desired probability is:

P(X \geq 2) = 1 - P(X < 2)

In which:

P(X < 2) = P(X = 0) + P(X = 1)

Then

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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P(X = 1) = C_{9,1}.(0.3333)^{1}.(0.6667)^{8} = 0.117

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.026 + 0.117 = 0.143

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.143 = 0.857

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

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