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

Read 2 more answers

if a rectangle has an area of 30 square meters and a perimeter of 34 meters . what is the dimensions of the rectangle?

timama [110]

P=2(L+W) and P=34 so

2(L+W)=34

L+W=17 so we can say

L=17-W

A=LW using L from above

A=(17-W)W

A=17W-W^2 and A=30 so

30=17W-W^2

W^2-17W+30=0

W^2-2W-15W+30=0

W(W-2)-15(W-2)=0

(W-15)(W-2)=0

So the dimensions of the rectangle are 15 meters by 2 meters.

7 0

3 years ago

lipka reads a book of 1/34 hrs everyday she reads the entire book in 6 days how many hours in all were required by her to read t

marshall27 [118]

Answer: She needs 10 1/2 hours to read the book.

Step-by-step explanation:I day = 1 3/4 hours

6 days = 1 3/4 x 6

6 days = 7/4 x 6

6 days = 42/4

6 days = 10 1/2 hours

8 0

2 years ago