- #1
Mogarrr
- 120
- 6
Homework Statement
A fair die is cast until a 6 appears. What is the probability that it must be cast more than five times.
Homework Equations
The die is fair, hence like most of the problems I can assume equally likely outcomes.
[itex]P(A^c)=1-P(A)[/itex] for any event A
The Attempt at a Solution
Theoretically, a 6 may never come up. It should be better to calculate the complement of the event.
The complement, I think, is the event in at least 5 tosses, a 6 occurs. So a 6 may occur in the 1st toss or the 2nd toss or... or the 5th toss.
So I have [itex] \frac 16 + \frac 56 \cdot \frac 16 + ... + (\frac 56)^4 \cdot \frac 16 [/itex]
Then factoring out [itex]\frac 16[/itex] and writing the probabilities as a summation, I have
[itex] \frac 16 \cdot \sum_{k=1}^5 (\frac 56)^{5-i} [/itex]
Is this correct? I don't have the answer. I suspect this can be derived from a probability distribution. If my suspicions are correct, which probability distribution?