Question

A biased coin, twice as likely to come up heads as tails, is tossed once. If it shows heads, a chip is drawn from urn I, which contains three white chips and four red chips; if it shows tails, a chip is drawn from urn II, which contains six white chips and three red chips. Given that a white chip was drawn, what is the probability that the coin came up tails.

Answer 1

`=(7)/(16)}`

Explanation:

`\mathrm{Let\;me\;denote\;Probability\;by\;P\;through\;out\;my\;answer}`

`\mathrm{Heads\rightarrow P(H)=(2)/(3)}`

`\mathrm{Head\Rightarrow Urn\;1}`

`\mathrm Heads)=(3)/(3+4)=(3)/(7)`

`\mathrm{Tails\rightarrow P(T)=(1)/(3)}`

`\mathrm Tails)=(6)/(3+6)=(6)/(9)`

`\mathrmWe\;now\;want\;P(Tails`

`\mathrm\Rightarrow \;P(Tails`

`\mathrmWhite\;Chip)=((2)/(3))/((2)/(3)+(6)/(7))=(14)/(32)=(7)/(16)`