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?