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irina1246 [14]
3 years ago
13

Small juice boxes come in packages of 6. Yogurt treats come in packages of 10. Paula wants to have the exact same number of each

item. How many bottles of juice and individual yogurt treats will she have altogether? How many packages of each will she need?
Mathematics
1 answer:
erastovalidia [21]3 years ago
8 0

if she buys 10 of the small juice box packages and six of the yogurt treat packages then she should have an even number of both. That would be 60 of each.

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Answer:

a) X \sim Binom(n=16, p=0.2)  

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Step-by-step explanation:

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The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Part a

Let X the random variable of interest, on this case we now that:  

X \sim Binom(n=16, p=0.2)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

The expected value is given by this formula:

E(X) = np=16*0.2=3.2

Part b

For this case we want this probability:

P(X=0)

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

And using this function we got:

P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815

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