Mathematics: 100 random students are surveyed outside of the student center on campus. Let V denote that the student has a Visa credit card and let M denote that the student has a Mastercard credit card. 40 people had a Visa card, 32 had a Mastercard, and 12 had both a Visa and Mastercard. Calculate the following. hade Visa care, 3a hace a mastercard, and 12 had both (a) P(M|V) =.(b) P(MCV) =. (c) P(VIM) =. (d) P(VC I M) =.

Step-by-step explanation:Step 1: DistributeStep 2: Subtract 20 from both sidesStep 3: Divide both sides by 15 ...

100 random students are surveyed outside of the

Ответ:

JAXKBOII55951

18.01.2022

Mathematics

(a) The value of P (M | V) is 0.30.

(b) The value of $P (M^{c} | V)$ is 0.70.

(d) The value of $P(V^{c}|M)$ is 0.625.

Step-by-step explanation:

It is provided that,

V = a student has a Visa card

M = a student has a Master card

N = 100, n (V) = 40, n (M) = 32 and n (V ∩ M) = 12.

The probability of a student having visa card is:

$P(V) = \frac{n(V)}{N}= \frac{40}{100}=0.40$

The probability of a student having master card is:

$P(M) = \frac{n(M)}{N}= \frac{32}{100}=0.32$

The probability of a student having visa card and a master card is:

$P(V\cap M) = \frac{n(V\cap M)}{N}= \frac{12}{100}=0.12$

The conditional probability of an event, say A, given that another event, say B, has already occurred is,

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

(a)

Compute the probability that a student has a master card given that he/she has a visa card also, i.e. P (M | V) as follows:

$P(M|V)=\frac{P(V\cap M)}{P(V)} =\frac{0.12}{0.40}=0.30$

Thus, the value of P (M | V) is 0.30.

(b)

Compute the probability that a student does not have a master card given that he/she has a visa card also, i.e. $P (M^{c} | V)$ as follows:

$P (M^{c} | V)=1-P(M|V)=1-0.30=0.70$

Thus, the value of $P (M^{c} | V)$ is 0.70.

(c)

Compute the probability that a student has a visa card given that he/she has a master card also, i.e. P (V | M) as follows:

$P(V|M)=\frac{P(V\cap M)}{P(M)} =\frac{0.12}{0.32}=0.375$

Thus, the value of P (V | M) is 0.375.

(d)

Compute the probability that a student does not have a visa card given that he/she has a master card also, i.e. $P(V^{c}|M)$ as follows:

$P(V^{c}|M)=1-P(V|M)=1-0.375=0.625$

Thus, the value of $P(V^{c}|M)$ is 0.625.

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Ответ:

johnsnow69

18.09.2020

Mathematics

x = 0.2

Step-by-step explanation:

Step 1: Distribute

5(3x + 4) = 23

(5 * 3x) + (5 * 4) = 23

(15x) + 20 = 23

Step 2: Subtract 20 from both sides

(15x) + 20 - 20 = 23 - 20

15x = 3

Step 3: Divide both sides by 15

$\frac{15x}{15} = \frac{3}{15}$

$x = \frac{1}{5}$

x = 0.2

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