A thermocouple placed in a certain medium produces readings within 0.1°C of the true temperature 70% of the time, readings more than 0.1°C above the true temperature 10% of the time, and readings more than 0.1°C below the true temperature 20% of the time.
a. In a series of 10 independent readings, what is the probability that 5 are within 0.1°C of the true temperature, 2 are more than 0.1°C above, and 3 are more than 0.1°C below?
b. What is the probability that more than 8 of the readings are within 0.1°C of the true temperature?
(a) Let 
be the number of readings that are within 0.1°C of the true temperature, let 
be the number of readings
that are more than 0.1°C above the true temperature, let 
be the number of readings that are more than 0.1°C
below the true temperature. Then
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