GATE CSE 2016 Set 2 | Question: 05

Question

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7$, and given that it is of Type $2$ is $0.4$. The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.

Answer 1

in this tree method remember there is a only one game. If you've identified what values to be assigned on edges then you've completed 90% of solution after that it's the matter of few seconds.

So from root(L->R we go/you can make top to bottom) WE FIRST SELECT LED then we check for life >100. 

hope it clears everything. TREE METHOD IS BEST FOR SOLVING CONDITIONAL PROBABILITY  (my opinion)

Answer 2

Final Answer is 0.55

Answer 3

Using Tree Method: