I am having trouble with this problem......
Find the probability of rolling a single die and getting a 5 in fewer then 4 rolls.
(You stop when you get a 5 )
Thanks in advance
I am having trouble with this problem......
Find the probability of rolling a single die and getting a 5 in fewer then 4 rolls.
(You stop when you get a 5 )
Thanks in advance
1st roll - 5 (1/6) or not a 5 (5/6)
2nd roll (5/6) - 5 (1/6) or not a 5 (5/6)
3rd roll (5/6)^2 - 5 (1/6) or not a 5 (5/6)
4th roll (5/6)^3 - 5 (1/6) or not a 5 (5/6)
5th roll (5/6)^4 - 5 (1/6) or not a 5 (5/6)
You decide where to stop and what it all means.
What you're looking for is the probability of getting a number '5' in less than 4 toses.
So that means there's only toss 1, toss2, toss 3.
For toss 1, P(5 on 1st roll) = 1/6
For toss 2, p(5 on 2nd roll) = (5/6)x(1/6)
For toss 3, p(5 on 3nd roll) = [(5/6)^2]x(1/6)
Since it's less than 4 toses, remember that you need to COUNT IN ALL THE FIRST 3 ROLLS.
THEN, you'll get 1/6 + (5/6)x(1/6) + [(5/6)^2]x(1/6) = 91/216
Okay?