die and coin

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 am; Thanked: 82 times; Followed by:9 members; GMAT Score:720

die and coin

by maihuna » Fri Aug 14, 2009 9:08 am

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.

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Source: Beat The GMAT — Problem Solving | Fri Aug 14, 2009 9:08 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Fri Aug 14, 2009 12:00 pm

Probabilities... Hmm... Strange question, but interesting nonetheless.

From 1 to 6 you get two multiples of 3: 3 and 6. You will need to get 3 and 6 for your first toss. Then it gets a bit more complicated (or at least that's what I understand from if any other number comes). If you got a 6 the first time, now you need a 3 and vice versa. The coin toss will be simpler, since there's a fixed 50% chance of getting tails.

So two cases, each with the same probability. Getting a 3 the first time is 1/6, while getting a 6 the second time is again 1/6. Getting the tails will be 1/2. The probability for this event will be 1/6 * 1/6 * 1/2 = 1/72. Use the same reasoning to conclude that getting a 6 the first time and a 3 the second time yields the same probability.

Add them up to get 1/72 + 1/72 = 2/72 = 1/36.

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kaulnikhil: Master | Next Rank: 500 Posts; Posts: 338; Joined: Fri Apr 17, 2009 1:49 am; Thanked: 9 times; Followed by:3 members

by kaulnikhil » Fri Aug 14, 2009 12:18 pm

s it 1/12??

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 am; Thanked: 82 times; Followed by:9 members; GMAT Score:720

by maihuna » Fri Aug 14, 2009 10:37 pm

DanaJ wrote:

Probabilities... Hmm... Strange question, but interesting nonetheless.

From 1 to 6 you get two multiples of 3: 3 and 6. You will need to get 3 and 6 for your first toss. Then it gets a bit more complicated (or at least that's what I understand from if any other number comes). If you got a 6 the first time, now you need a 3 and vice versa. The coin toss will be simpler, since there's a fixed 50% chance of getting tails.

So two cases, each with the same probability. Getting a 3 the first time is 1/6, while getting a 6 the second time is again 1/6. Getting the tails will be 1/2. The probability for this event will be 1/6 * 1/6 * 1/2 = 1/72. Use the same reasoning to conclude that getting a 6 the first time and a 3 the second time yields the same probability.

Add them up to get 1/72 + 1/72 = 2/72 = 1/36.

Answer is 0.

Charged up again to beat the beast

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DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770