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: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)= 0.63The probability that a student has a MasterCard (event M) is P(M)= 0.11The 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.