Find the probabilities of​ A, B,​ C, and​ D, and determine​ which, if​ any, pairs of these events are independent.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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In three independent flips of a coin where there is a 63​% chance of flipping a tail​, let A denote​ {first flip is a tail​}, B denote​ {second flip is a tail​}, C denote​ {first two flips are tail​s}, and D denote​ {three tails on the first three​ flips}. Find the probabilities of​ A, B,​ C, and​ D, and determine​ which, if​ any, pairs of these events are independent.

​P(A)=
​(Round to two decimal places as​ needed.)
 
​P(B)=
​(Round to two decimal places as​ needed.)
 
​P(C)=
​(Round to four decimal places as​ needed.)
 
​P(D)=
​(Round to four decimal places as​ needed.)
 
Which of these pairs of events are​ independent?
 
A. Events A and B because​ P(A and B)=​P(A)•​P(B).
 
B. Events A and C because​ P(A and C)=​P(A)•​P(C).
 
C. None of the pairs of events are independent.
 
D. Events C and D because​ P(C and D)=​P(C)•​P(D)
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