Answer: see answers below
Explanation:
(i) The first leaf of the tree is: black = 5/9 and white = 4/9
That means that there are 5 black marbles out of 9 total marbles and 4 white marbles out of 9 total marbles.
Total marbles = 9
Black marbles = 5
White marbles = 4
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(ii)
P(B₂/B₁)
The probability that the 2nd marble is black given that the 1st marble was black.
P(W₂/B₁)
The probability that the 2nd marble is white given that the 1st marble was black.
P(B₂/W₁)
The probability that the 2nd marble is black given that the 1st marble was white.
P(W₂/W₁)
The probability that the 2nd marble is white given that the 1st marble was white.
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(iii) Outcomes (iv) Probability
(B, B) (5/9) x (1/2) = 5/18
(B, W) (5/9) x (1/2) = 5/18
(W, B) (4/9) x (5/8) = 5/18
(W, W) (4/9) x (3/8) = 3/18
Check: Total = 18/18 = 1
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(iv) Dependent
Once the first ball is drawn, there is one less ball for the second draw. Therefore, the second draw is dependent on the first draw.