An insurer estimates that Smiths time until death is uniform

An insurer estimates that Smith\'s time until death is uniformly distributed on the interval [0,5] and Jones\' time until death is uniform on the interval [0,10]. The insurer assumes that the two times of death are independent of one another. Find the probability that Smith is the first of the two to die.

Answer Choices are:         A) 1/4       B) 1/3       C) 1/2     D) 2/3      E)   3/4

Solution

let us assume the cases as rectangle with length 10 with y axisand breadth 5 with x axis

the area we want is x<y

we get 25/100

probability is 1/4