A radioactive material emits [math]\alpha[/math]-particles at a rate described by the density function

[[math]] f(t) = .1e^{-.1t}\ . [[/math]]

Find the probability that a particle is emitted in the first 10 seconds, given that

• no particle is emitted in the first second.
• no particle is emitted in the first 5 seconds.
• a particle is emitted in the first 3 seconds.
• a particle is emitted in the first 20 seconds.