Question

The probability that a student has a Visa card (event V) is .63. The probability that a student has a MasterCard (event M) is .11. The probability that a student has both cards is .03. (a) Find the probability that a student has either a Visa card or a MasterCard. (Round your answer to 2 decimal places.) Probability .77 .77 Incorrect (b) In this problem, are V and M independent

Answer 1

To find the probability that a student has either a Visa card or a MasterCard, add the probabilities of each card and subtract the probability of having both. The probability is 0.71.

Step-by-step explanation:

To find the probability that a student has either a Visa card or a MasterCard, we can use the formula:

P(V or M) = P(V) + P(M) - P(V and M)

Plugging in the given probabilities, we have:

P(V or M) = 0.63 + 0.11 - 0.03 = 0.71

Therefore, the probability that a student has either a Visa card or a MasterCard is 0.71.

In this problem, V and M are not independent because the probability of having a MasterCard is affected by whether or not the student already has a Visa card. If they were independent, the probability of having both cards would be the product of the individual probabilities, which is not the case here.

Answer 2

a) The probability that a student has either a Visa card or a MasterCard is 0.71.

b) V and M are not independent.

Step-by-step explanation:

Given : The probability that a student has a Visa card (event V) is 0.63. The probability that a student has a MasterCard (event M) is 0.11. The probability that a student has both cards is 0.03.

To find :

a) The probability that a student has either a Visa card or a MasterCard ?

b) In this problem, are V and M independent ?

Solution :

The probability that a student has a visa card(event V) is P(V)= 0.63

The probability that a student has a MasterCard (event M) is P(M)= 0.11

The probability that a student has both cards is
`P(V \cap M)=0.03`

a) Probability that a student has either a Visa card or a Master Card is given by,

`P(V \cup M) = P(V) + P(M) - P(V\cap M)`

`P(V \cup M) = 0.63+ 0.11- 0.03`

`P(V \cup M) =0.74- 0.03`

`P(V \cup M) =0.71`

The probability that a student has either a Visa card or a MasterCard is 0.71.

b) Two events, A and B, are independent if
`P(A\cap B)=P(A)P(B)`

For V and M to be independent the condition is satisfied,

`P(V\cap M)=P(V)P(M)`

Substitute the values,

`0.03=0.63* 0.11`

`0.03\\eq 0.0693`

So, V and M are not independent.