Suppose you have a flashlight that uses 2 batteries and a package of 3 new batteries. Suppose that each battery has an independent lifetime (in hours) with exponential distribution. Find the distribution of the number of hours T that you can use the flashlight.

My thoughts are:

P(T = t) = P(2 of the batteries have lifetimes of t hours)

= P(X = t, Y = t) + P(X = t, Z = t) + P(Y = t, Z = t)

=

= 3

Could someone tell me if this is correct?