Factory X's bulbs work for over 4000 hours in 59% of cases, whereas factory Y's bulbs work for over 4000 hours in 65% of cases. It is known that factory X supplies 60% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 4000 hours? Choose the correct choice from the following
A) 66.4%  B) 61.4%  C) 77.4%  D) 65%  E) 53.9%
For X, 60% of 59% will work.   For Y, 40% of 65% will work. *40% is the rest of the bulb supply in the market.   So, the probability that a purchased bulb will work is:   0.60(0.59) = .354   0.40(0.65) = 0.26   The combined probability then is 35.4 + 26.00= 
<gadget id="calculator">35.4 + 26.00</gadget>
<output>61.4</output>
61.4%   ANS 61.4%
<result>B</result>
Factory X's bulbs work for over 4000 hours in 59% of cases, whereas factory Y's bulbs work for over 4000 hours in 65% of cases. It is known that factory X supplies 60% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 4000 hours?