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) =.

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

(b) The value of is 0.70.

(c) The value of P (V | M) is 0.375.

(d) The value of 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:

The probability of a student having master card is:

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

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

(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:

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. as follows:

Thus, the value of 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:

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. as follows:

Thus, the value of is 0.625.

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: