A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 w

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 white. The pointer is spun and a marble is picked at random.

a) Use a tree diagram to list the possible outcomes.

1. A, Grey
2. A, Black
3. A, White
4. B, Grey
5. B, Black
6. B, White
7. C, Grey
8. C, Black
9. C, White

b) What is the probability of:

i) spinning A?
P(A) = Number of A sections on spinner / Total Sections
P(A) = 1/3
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ii) picking a grey marble?
P(A) = Number of grey marbles / Total Marbles
P(A) = 1/3
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iii) spinning A and picking a white marble?
Since they're independent events, we multiply to get:
P(A AND White) = P(A) * P(White)
P(A) was found in i) as 1/3

Find P(White):
P(White) = Number of white marbles / Total Marbles
P(White) = 1/3

Therefore, we have:
P(A AND White) = 1/3 * 1/3
P(A AND White) = 1/9
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iv) spinning C and picking a pink marble?
Since they're independent events, we multiply to get:
P(C AND Pink) = P(C) * P(Pink)

Find P(C):
P(C) = Number of C sections on spinner / Total Sections
P(C) = 1/3

Find P(Pink):
P(Pink) = Number of pink marbles / Total Marbles
P(Pink) = 0/3

Therefore, we have:
P(C AND Pink) = 1/3 * 0
P(C AND Pink) = 0