There are two dice A & B. Die A has 4 red and 2 white faces and B has 2 red and 4 white faces. A coin is tossed once. If it shows head, die A is rolled if it shows tail. Die B is rolled, if the probability that die A is used is $\frac{32}{33},$ when it is given that red turns up every time in first n – throws then n is equal to

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answer is D.

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Detailed Solution

$P (\frac{R}{E_{1}}) = {(\frac{2}{3})}^{n}, P (\frac{R}{E_{2}}) = {(\frac{1}{3})}^{n} \Rightarrow P (\frac{E_{1}}{R}) = \frac{P (E_{1}) P (\frac{R}{E_{1}})}{P (E_{1}) P (\frac{R}{E_{1}}) + P (E_{2}) P (\frac{R}{E_{2}})}$

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