Problem Solving

ani781 wrote:string of 10 lightbulbs is wired in such a way that if
any individual lightbulb fails, the entire string fails. If for
each individual lightbulb the probability of failing during
time period T id 0.06, what is the probability that the
string of lightbulbs will fail during time period T?

A.0.06
B.(0.06)^10
C.1-(0.06)^10
D.(0.94)^10
E.1-(0.94)^10

Aside: If P(bulb fails) = 0.06, then P(bulb doesn't fail) = 0.94


Okay, the entire string of lightbulbs will fail if 1 or more lightbulbs fail.
So, we want P(at least 1 lightbulb fails)

When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
P(at least 1 lightbulb fails) = 1 - P(zero lightbulbs fail)


P(zero lightbulbs fail)
P(zero lightbulbs fail) = P(1st bulb doesn't fail AND 2nd bulb doesn't fail AND 3rd bulb doesn't fail AND . . . AND 9th bulb doesn't fail AND 10th bulb doesn't fail)
= P(1st bulb doesn't fail) x P(2nd bulb doesn't fail) x P(3rd bulb doesn't fail) x . . . x P(9th bulb doesn't fail) x P(10th bulb doesn't fail)
= (0.94) x (0.94) x (0.94) x . . . x(0.94) x (0.94)
= (0.96)^10

So, P(at least 1 lightbulb fails) = 1 - P(zero lightbulbs fail)
= 1 - (0.94)^10
= E

Cheers,
Brent

ani781 wrote:Thanks a lott Brent. Now this makes it very clear to me.

Is it possible for you to point me at some similar or almost in the same line of questions ? Or perhaps you can guide me to some more of these questions to further solidify my understanding ?


Thanks in advance.

[/quote]

Sure thing.
Try these:
- https://www.beatthegmat.com/how-to-solve ... 16924.html
- https://www.beatthegmat.com/probability- ... 21264.html
- https://www.beatthegmat.com/probability- ... 23109.html
- https://www.beatthegmat.com/bird-t265208.html
- https://www.beatthegmat.com/probability-t264072.html

Cheers,
Brent