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Re: Daniel is playing a dice game in which [#permalink]
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Why could this not be a case of 1 - the probability that 4 does not come in any of the remaining three throws?
1- (5/6)x(5/6)x(5/6) = 1 - (125/216) = 81/216
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Re: Daniel is playing a dice game in which [#permalink]
vedantmodi wrote:
Why could this not be a case of 1 - the probability that 4 does not come in any of the remaining three throws?
1- (5/6)x(5/6)x(5/6) = 1 - (125/216) = 81/216


You are not considering the case where, with the remaining 3 tries, we can get another number 3 times
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Re: Daniel is playing a dice game in which [#permalink]
tHANKS FOR THE HELP
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Re: Daniel is playing a dice game in which [#permalink]
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vedantmodi wrote:
Why could this not be a case of 1 - the probability that 4 does not come in any of the remaining three throws?
1- (5/6)x(5/6)x(5/6) = 1 - (125/216) = 81/216


It is a bit different.
Scenario 1 ---> All 3 rolls are different from the first two ---> (5/6)*(5/6)*(5/6) = 125/216

Scenario 2 ---> All 3 rolls are different from the first two BUT same (also win) ---> (5/6)*(1/6)*(1/6) = 5/216

Scenario 3 ---> Two rolls are same as the first two rolls (lose because only EXACTLY same numbers count as a win) ---> (5/6)*(1/6)*(1/6)*3 = 15/216

Scenario 4 --->All 3 rolls are SAME from the first two (lose because only EXACTLY same numbers count as a win) ---> (1/6)*(1/6)*(1/6)*3 = 1/216

1 - 125/216 + 5/216 - 15/216 - 1/216 = 80/216
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Daniel is playing a dice game in which [#permalink]
This one is quite tricky! So for us to win, we have to get a 4 on exactly one but no more than one of the remaining throws, OR we need to get exactly three 1s, exactly three 2s, exactly 3 threes, exactly three 5s, or exactly three 6s.

Getting 4 on exactly 1 of the remaining throws and not on the other 2 throws = (1/6)(5/6)(5/6)*3 (multiplying by 3 since the 4 could be in any of the three remaining rolls) = 75/216.

For getting 5 of the same value (NOT equal to 4) on all remaining throws = (1/6)^3 * 5 = 5/216.

Total = (75+5)/216=80/216.
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Re: Daniel is playing a dice game in which [#permalink]
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Re: Daniel is playing a dice game in which [#permalink]
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