For each party, there are only two possible outcomes. Either they will order drinks with their meal, or they will not. The probability of a party ordering drinks with their meal is independent of other parties. So 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.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal.

This means that $p = 0.75$

During one hour, Ryan served 6 parties. Assuming that each party is equally likely to order drinks, what is the probability that at least one party will not order drinks?

6 parties, so n = 6.

Either all parties will order drinks, or at least one will not. The sum of the probabilities of these events is decimal 1. So

$P(X = 6) + P(X < 6) = 1$

We want P(X < 6). So

$P(X < 6) = 1 - P(X = 6)$

In which

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

$P(X = 6) = C_{6,6}.(0.75)^{6}.(0.25)^{0} = 0.18$

$P(X < 6) = 1 - P(X = 6) = 1 - 0.18 = 0.82$

0.82 = 82% probability that at least one party will not order drinks

5 0

3 years ago

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Jona and his friend go apple picking .jonah fills 5 basket.each basket holds 15apples . If 4 of jonah's friend pick the same amo

k0ka [10]

5 baskets...each holds 15 apples....(5 x 15) = 75 apples

4 friends pick the same amount...
4 x 75 = 300 apples picked in total. <==

5 0

3 years ago

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What is the answer? <br>x+y=15 <br>-2x+5y=-2

zavuch27 [327]

Multiply the first equation by 2

2x + 2y =30

now we’ll add the second equation to the first equation

2x + 2y =30
-2x+5y= -2

7y=28

divide by 7

y=4

now plug y back into the first equation

x + 4 = 15

subtract 4

x=11

6 0

3 years ago