- #1

songoku

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- Homework Statement
- A fair five-sided spinner is numbered 3, 4, 5,6, and 7. The spinner is spun and the number showing, X, is recorded. The spinner is spun until it gets an odd number or until it has been spun 3 times. The number of spins taken to get an odd number, Y, is recorded.

Find P(X > Y + 3)

- Relevant Equations
- Probability

I divide the question into three cases:

1) P (Y = 1 and X = 5 or 7) = 1/5 + 1/5 = 2/5

2) P(Y = 2 and 1st spin = even and 2nd spin = 7) = 2/5 x 1/5 = 2/25

3) P(Y = 3 and 1st and 2nd spin = even and 3rd spin = 7) = 2/5 x 2/5 x 1/5 = 2/125

Total probability = 2/5 + 2/25 + 2/125 = 62/125

But the answer key is 61/125

Where is my mistake? Thanks

1) P (Y = 1 and X = 5 or 7) = 1/5 + 1/5 = 2/5

2) P(Y = 2 and 1st spin = even and 2nd spin = 7) = 2/5 x 1/5 = 2/25

3) P(Y = 3 and 1st and 2nd spin = even and 3rd spin = 7) = 2/5 x 2/5 x 1/5 = 2/125

Total probability = 2/5 + 2/25 + 2/125 = 62/125

But the answer key is 61/125

Where is my mistake? Thanks