Answer:
a)

And replacing we got:

b)
And adding we got:
c)

And replacing we got:

Explanation:
Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part a
We want to find this probability:

And replacing we got:

Part b

And adding we got:
Part c

And replacing we got:
