Respuesta :
Answer:
(a) The value of P (M | V) is 0.30.
(b) The value of [tex]P (M^{c} | V)[/tex] is 0.70.
(c) The value of P (V | M) is 0.375.
(d) The value of [tex]P(V^{c}|M)[/tex] 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:
[tex]P(V) = \frac{n(V)}{N}= \frac{40}{100}=0.40[/tex]
The probability of a student having master card is:
[tex]P(M) = \frac{n(M)}{N}= \frac{32}{100}=0.32[/tex]
The probability of a student having visa card and a master card is:
[tex]P(V\cap M) = \frac{n(V\cap M)}{N}= \frac{12}{100}=0.12[/tex]
The conditional probability of an event, say A, given that another event, say B, has already occurred is,
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
(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:
[tex]P(M|V)=\frac{P(V\cap M)}{P(V)} =\frac{0.12}{0.40}=0.30[/tex]
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. [tex]P (M^{c} | V)[/tex] as follows:
[tex]P (M^{c} | V)=1-P(M|V)=1-0.30=0.70[/tex]
Thus, the value of [tex]P (M^{c} | V)[/tex] 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:
[tex]P(V|M)=\frac{P(V\cap M)}{P(M)} =\frac{0.12}{0.32}=0.375[/tex]
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. [tex]P(V^{c}|M)[/tex] as follows:
[tex]P(V^{c}|M)=1-P(V|M)=1-0.375=0.625[/tex]
Thus, the value of [tex]P(V^{c}|M)[/tex] is 0.625.
