Probability rules..

Probability Level 4

A signal which can be green or red with probability 4 5 \frac{4}{5} and 1 5 \frac{1}{5} respectively, is received by station A A and then transmitted to station B B , The probability of each station receiving the signal correctly is 3 4 \frac{3}{4} .If the signal received at station B B is green, then the probability that the original signal was green is k k .

Find 46 k mod 37 \displaystyle{46k~ \text{mod}~ 37}

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The answer is 3.

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

The Cases are (order is Signal → \rightarrow Station A → \rightarrow Station B.

  1. Green , Green , Green
  2. Green , Red , Green
  3. Red , Green , Green
  4. Red , Red , Green

After this use conditional probablity.

You get k = 40 46 k = \frac{40}{46}

46 k = 40 46k = 40

40 m o d 37 = 3 40 \mod 37 = \boxed{3}

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