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# Solving questions on probability

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1. 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.
2. (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
3. (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
0.8

125/216

what do you mean?
4. (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.
5. (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.
6. 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?
7. (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?

8. bump
9. (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?

Apart from a x needing to be a /

yes

10. does plain = dark
11. PPW
PWP
WPP

each have the same probability

work it out and x3
12. (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
13. (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
14. (Original post by TenOfThem)
The denominator needs to change as each time you chose one you have fewer to chose from
oh ok so its 6/20x5/19x4/18=120/6840 x3=0.053
15. (Original post by TenOfThem)
The denominator needs to change as each time you chose one you have fewer to chose from
just checking if my answer is correct above.
16. (Original post by non)
just checking if my answer is correct above.

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