1 Over a period of time, radioactive substances decay into other substances. During this decay a Geiger counter can be used to detect the number of radioactive particles that the substance emits. A certain radioactive source is decaying at a constant average rate of 6.1 particles per 10 seconds. The particles are emitted randomly and independently of each other.

1. State a distribution which can be used to model the number of particles emitted by the source in a 10-second period.
2. State the variance of this distribution.
3. Find the probability that at least 6 particles are detected in a period of 10 seconds.
4. Find the probability that at least 36 particles are detected in a period of 60 seconds.
5. Another radioactive source emits particles randomly and independently at a constant average rate of 1.7 particles per 5 seconds. Find the probability that at least 10 but no more than 15 particles are detected altogether from the two sources in a period of 10 seconds.