Question

Please solve this question!​

Answer 1

Answer:  see answers below

Step-by-step 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  $\checkmark$

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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.