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Solving questions on probability

Q1 gambling game has 3 reels which rotate independently they stop randomly at pics of fruit. probability of lemon is 0.2. a prize is won if you get 3 lemons.

someone gets 4 attempts. calc the prob that he fails on first 3 attempts and wins on fourth.

Q2 throw 3 sixes to win. someone has 5 attempts. what is the prob that he looses 4 attempts and win fifth?

Q3 box contains 20 chocs. 6 are dark, 10 are milk and 4 are white. he eats 3 taken at random. calc prob that 2 are plain and one is white.
(edited 11 years ago)
Reply 1
Avatar for sputum
sputum
9
Original post by non
Q1 gambling game has 3 reels which rotate independently they stop randomly at pics of fruit. probability of lemon is 0.2. a prize is won if you get 3 lemons.

someone gets 4 attempts. calc the prob that he fails on first 3 attempts and wins on fourth.


What's the probability he fails on his first attempt?

Q2 throw 3 sixes to win. someone has 5 attempts. what is the prob that he looses 4 attempts and win fifth?


What's the probability of throwing 3 sixes?

Q3 box contains 20 chocs. 6 are dark, 10 are milk and 4 are white. he eats 3 taken at random. calc prob that 2 are plain and one is white.


saving this one for later:smile:
Reply 2
Avatar for non
non
OP
15
Original post by sputum
What's the probability he fails on his first attempt?



What's the probability of throwing 3 sixes?



saving this one for later:smile:


0.8

125/216

what do you mean?
Reply 3
Avatar for sputum
sputum
9
Original post by non
0.8
yes. so what is the probability he fails three times in a row?

125/216

I'm not sure how you came up with this but I phrased the question badly.

Actually the original question is not clear as to how many dice the guy is throwing, I was assuming three sixes from three dice.

what do you mean?


it's a bit more complicated because you can pick 2 plain and 1 white in more than one way.
Reply 4
Avatar for non
non
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15
Original post by sputum
yes. so what is the probability he fails three times in a row?


I'm not sure how you came up with this but I phrased the question badly.

Actually the original question is not clear as to how many dice the guy is throwing, I was assuming three sixes from three dice.



it's a bit more complicated because you can pick 2 plain and 1 white in more than one way.


0.8x0.8x0.8?

1/6 x 1/6 x 1/6

Whats the best way to work out this question?
And thanks for the help so far. :smile:
Reply 5
Avatar for sputum
sputum
9
OK so the first one you multiply what you got so far by the probability of a win and you're done.

The second one is easily done using the fact that the two probabilities sum to 1 (so the probability of a success is 1- the probability of a failure)

The third one you can do in a few ways. Have you done combinations?
Reply 6
Avatar for non
non
OP
15
Original post by sputum
OK so the first one you multiply what you got so far by the probability of a win and you're done.

The second one is easily done using the fact that the two probabilities sum to 1 (so the probability of a success is 1- the probability of a failure)

The third one you can do in a few ways. Have you done combinations?


Is the probability of winning dice dice game 1/216? Because that's 1/6x1/6x1/6
So 4 loses is 215/216x215/216x215/216x215x216?
And one win so x 1/216

You can make it up by one plain one plain one white
One white one plain one plain
Are there any other ways?

Thanks for your help
Reply 7
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non
OP
15
bump
Reply 8
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TenOfThem
18
Original post by non
Is the probability of winning dice dice game 1/216? Because that's 1/6x1/6x1/6
So 4 loses is 215/216x215/216x215/216x215x216?
And one win so x 1/216

You can make it up by one plain one plain one white
One white one plain one plain
Are there any other ways?

Thanks for your help



Apart from a x needing to be a /

yes

215216×215216×215216×215216×1216 \frac{215}{216} \times \frac{215}{216} \times \frac{215}{216} \times\frac{215}{216} \times\frac{1}{216}
Reply 9
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TenOfThem
18
does plain = dark
PPW
PWP
WPP

each have the same probability

work it out and x3
Reply 11
Avatar for non
non
OP
15
Original post by TenOfThem
PPW
PWP
WPP

each have the same probability

work it out and x3


thank you so much. so would it be. 6/20x6/20x4/20=144/8000 x3=0.054
Original post by non
thank you so much. so would it be. 6/20x6/20x4/20=144/8000 x3=0.054


The denominator needs to change as each time you chose one you have fewer to chose from :smile:
Reply 13
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non
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15
Original post by TenOfThem
The denominator needs to change as each time you chose one you have fewer to chose from :smile:


oh ok so its 6/20x5/19x4/18=120/6840 x3=0.053
Reply 14
Avatar for non
non
OP
15
Original post by TenOfThem
The denominator needs to change as each time you chose one you have fewer to chose from :smile:


just checking if my answer is correct above.
Original post by non
just checking if my answer is correct above.


:smile:

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