GATE CSE
First time here? Checkout the FAQ!
x
+4 votes
997 views
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 _________.
asked in Probability by Veteran (41.9k points)  
edited by | 997 views

2 Answers

+14 votes
Best answer

Suppose that a shop has an equal number of LED bulbs of two different types.  ==> Therefore

Probability of Taking Type 1 Bulb => 0.5

Probability of Taking Type 2 Bulb => 0.5

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.

Prob(100+ | Type1) => 0.7

Prob(100+| Type2) => 0.4

Prob(100+) => Prob(100+ | Type1) * Prob(Type1) + Prob(100+ | Type2) * Prob(Type2)

                = 0.7 * .5 + .4 * .5

                = 0.55

answered by Veteran (41.9k points)  
selected by
I submitted 0.5 is it correct then? :/
Nope
Ok :/
tree approach is best fr this kind of question....
Can you please once draw the tree for it?
+13 votes
SIMPLY-

TYPE-1 bulbs ===>let total =10 then 7 are going for 100 years

TYPE-2 bulbs====>let total=10 then 4 are going for 100 years

TOTAL==>20 out of which 11 are going for 100 years ..THEREFORE probability=11/20=.55
answered by Active (1.8k points)  
nice approach :)
Answer:

Related questions



Top Users Jul 2017
  1. Bikram

    4910 Points

  2. manu00x

    2940 Points

  3. Debashish Deka

    1870 Points

  4. joshi_nitish

    1776 Points

  5. Arjun

    1506 Points

  6. Hemant Parihar

    1306 Points

  7. Shubhanshu

    1128 Points

  8. pawan kumarln

    1124 Points

  9. Arnab Bhadra

    1114 Points

  10. Ahwan

    956 Points


24,099 questions
31,074 answers
70,703 comments
29,407 users