Use the Venn diagram to calculate probabilities.

Mathematics

2 answers:

sergejj [24]4 years ago

6 0

1. The number of elements of the universal set, or the sample space is 59

2. P(A|C) is the probability of A to happen once we know C has occured

it is calculated using the formula P(A|C) = P(A ∩ C) / P(C) = (14/59)/(21/59)=14/21=2/3

3. P(C|B) = P(C ∩ B) / P(B) = (11/59)/(27/59)=11/27

4. P(C)=(6+8+3+4)/59=21/59

5. P(B|A) = P(B ∩ A) / P(A) = (13/59)/(31/59)=13/31

Correct answer: P(A|C) = 2/3

Vlad [161]4 years ago

5 0

Total number of elements in the set =59.

1)P(A|C) = P(A ∩ C) / P(C) = $\frac{14}{21}=\frac{2}{3}$

2)P(C|B) = P(C ∩ B) / P(B) = $\frac{11}{27}$

3) P(A) = $\frac{31}{59}.$

4)P(C) = $\frac{21}{59}.$

5)P(B|A)=P(B ∩ A) / P(A)= $\frac{13}{31}$

Options 1 and 3 are right.

You might be interested in

A restaurant charges an automatic gratuity of 18% on tables with more than 6 people. A party of 8 had a bill of p. Which express

Nuetrik [128]

The expression of total cost of bill for party by 8 people in the restaurant including the gratuity amount is 1.18p.

<h3>How to write algebraic expression? </h3>

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

Steps to write down the simple algebraic expression-

Identify all the factors of the expression.

Assume a variable for the changing values.

Put a coefficient for the variable, if there is any rate of change of variable.

Use constant numbers for the fixed values.

Given information-

The automatic gratuity charges by restaurant is of 18 percent for more than 6 people on a table.

The number of people party in the restaurant is 8.

The bill amount of the 8 people for party in the restaurant is p.

Here, automatic gratuity charged by restaurant is of 18 percent for more than 6 people on a table

As the number of people party in the restaurant is 8 therefore the automatic gratuity charged by restaurant on the bill amount of p is should be 18 percent of it.

The 18 percent of bill p is,

$p\times\dfrac{18}{100} =0.18p$

Thus the gratuity charged by restaurant on the bill amount of p is 0.18 p.

Suppose the expression which is used to find the total cost of the meal with the gratuity is $f(p)$ .

Now the total bill amount should be equal to the sum of bill amount and gratuity amount. Thus, total cost of the meal with the gratuity is,

$f(p)=p+0.18p\\f(p)=1.18p$