Question

vacuum tube belongs to one of the three parties with probabilities of 0.25: 0.5: 0.25, respectively. The probability that the lamp will work a specified number of hours, respectively equal to those parties: 0.1: 0.2: 0.4 Determine the probability that the lamp is taken at random will work a specified number of hours.

Answer 1

@reemii

Answer 2

We know
Part 1 : P1, P(P1) = 1/4
Part 2 : P2, P(P2) = 1/2
Part 3 : P3, P(P3) = 1/4
and
P(work N hours | P1) = 0.1
P(work N hours | P2) = 0.2
P(work N hours | P3) = 0.4

The question is `P(work) = ?`
It's not Bayes' formula since you don't want to compute a conditional probbility. Which is it?

Answer 3

you mean which formula to use ?

Answer 4

yes

Answer 5

there is a formula like this two people's name on it. i don't remember the name.

Answer 6

am i close to the formula ?

Answer 7

The `Total probability formula` is the one to use.

Were you thinking about Bienaimé-Tchebichev ?

Answer 8

No, i think the names were different.

Answer 9

anyways, thanks for the help again.

Answer 10

Np.
it's "logically" the Total-probability-formula because you want to compute P(W) and you know only P(W|A), P(W|B), P(W|C), ..... where A,B,C,... divide the 'whole thing'.