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Aleks [24]
3 years ago
9

A diner has collected data about customer coffee-drinking habits. They have calculated that P(cream) = 0.5, P(sugar) = 0.6, and

P(cream or sugar) = 0.7. Determine the P(cream and sugar).
A) 0.4
B) 0.5
C) 0.6
D) 0.7
Mathematics
2 answers:
Nata [24]3 years ago
8 0

Answer: 0.4

Step-by-step explanation:

Given:  P(cream) = 0.5

P(sugar) = 0.6

P(cream or sugar) = 0.7

We know that to calculate probability of event A or B we apply the formula below:

\text{P(A or B)=P(A)+P(B)-P(A and B)}\\\\\Rightarrow \text{P(A and B)=P(A)+P(B)-P(A or B)}

\Rightarrow\text{P(cream and sugar)= P(cream)+P(sugar) -P(cream or sugar)}\\\\\Rightarrow\text{P(cream and sugar)}=0.5+0.6-0.7 \\\\\Rightarrow\text{P(cream and sugar)}=0.4

Anestetic [448]3 years ago
4 0
The <u>correct answer</u> is:

A) 0.4

Explanation:

The probability of cream, P(C), is 0.5.
The probability of sugar, P(S), is 0.6.
The probability of cream or sugar, P(C or S), is 0.7.

The union of probabilities (probability of two items using "or") is given by the formula:

P(A or B) = P(A) + P(B) - P(A and B)

For our problem, we have:
P(C or S) = P(C) + P(S) - P(C and S)

Using our information above, we have:
0.7 = 0.5 + 0.6 - P(C and S)

Combining like terms, we have:
0.7 = 1.1 - P(C and S)

Subtract 1.1 from each side:
0.7 - 1.1 = 1.1 - P(C and S) - 1.1
-0.4 = -P(C and S)

Divide both sides by -1:
-0.4/-1 = -P(C and S)/-1
0.4 = P(C and S)
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artcher [175]

Answer:

1) 20.

2) 30.

3) 47.

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Step-by-step explanation:

The order of operations consist in, first, evaluate the parenthesis, then the exponents, the multiplication, the division, and as last the addition and subtraction. Having this in mind:

1) (28 ÷ 4) + 3 + (10 - 8) × 5

7 + 3 + 2 × 5

7 + 3 + 10

20

2) 12 - 5 + 6 × 3 + 20 ÷ 4

12 - 5 + 18 + 5

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24 + 10 - 7

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6 0
4 years ago
Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean valu
Sauron [17]

Answer:

(1) 0.4207

(2) 0.7799

Step-by-step explanation:

Given,

Mean value,

\mu = 15.0

Standard deviation,

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= 1- P(\frac{x-\mu}{\sigma} \leq \frac{17.5-\mu}{\sigma})

=1-P(z\leq \frac{17.5 - 15}{1.25})

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=1-P(z\leq 2)

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= 0.4207

(2) P(14 ≤ X ≤ 18) = P(X ≤ 18) - P(X ≤ 14)

=P(z\leq \frac{18 - 15}{1.25}) - P(z\leq \frac{14 - 15}{1.25})

=P(z\leq \frac{3}{1.25}) - P(z\leq -\frac{1}{1.25})

=P(z\leq 2.4) - P(z\leq -0.8)

= 0.9918 - 0.2119

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