Independent solution

How to solve this Discrete Random Variables question

Setup

Setup

Let p_k be the probability of exactly k events, and let p_{4+} collect all counts of four or more.

p1+p2=0.250p_1+p_2=0.250
p2+p3=0.036p_2+p_3=0.036
p1+p2+p3+p4+=0.260p_1+p_2+p_3+p_{4+}=0.260
p4+=0.002p_{4+}=0.002

Model

Model

Subtract the first range and the upper tail from the at-least-one probability to isolate the three-count cell.

p3=0.260−0.250−0.002=0.008p_3=0.260-0.250-0.002=0.008

Compute

Compute

Remove the recovered three-count probability from the second overlapping range.

p2=0.036−p3p_2=0.036-p_3
p2=0.036−0.008=0.028p_2=0.036-0.008=0.028

Answer

Answer

The probability of exactly two events is 0.028.

0.028(D)\boxed{0.028\quad\text{(D)}}