Respuesta :
Answer:
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 [tex]P(V \cap M)=0.03[/tex]
a) Probability that a student has either a Visa card or a Master Card is given by,
[tex]P(V \cup M) = P(V) + P(M) - P(V\cap M)[/tex]
[tex]P(V \cup M) = 0.63+ 0.11- 0.03[/tex]
[tex]P(V \cup M) =0.74- 0.03[/tex]
[tex]P(V \cup M) =0.71[/tex]
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 [tex]P(A\cap B)=P(A)P(B)[/tex]
For V and M to be independent the condition is satisfied,
[tex]P(V\cap M)=P(V)P(M)[/tex]
Substitute the values,
[tex]0.03=0.63\times 0.11[/tex]
[tex]0.03\neq 0.0693[/tex]
So, V and M are not independent.
