Deepika is taking a probability class and at the end of each week she can be either up-to-date or she may have fallen behind. If she is up-to-date in a given week, the probability that she will be up-to-date or behind in the next week with respective probabilities 0.8 and 0.2. If she is behind in a given week, the probability that she will be up-to-date or behind in the next week with respective probabilities 0.6 and 0.4. Deepika (by default) up-to-date when she starts the class. If the probability that she is up-to-date after three weeks is P then the value of 100P equals

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answer is 75.2.

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Detailed Solution

$\begin{array}{l} R . P = P = (0.8) (0.8) (0.8) + (0.8) (0.2) (0.6) + (0.2) (0.6) (0.8) + (0.2) (0.4) (0.6) = 0.752 \\ ∴ 1000 P = 75.20 \end{array}$

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