If one bulb in a string of holiday lights fails to work, the whole
string will not light. If each bulb in a set has a 99.5% chance of working, what
is the maximum number of lights that can be strung together with at least a
90% chance of the whole string lighting?
the key is 21

Question

anonymous · Answer

Key is 21 wth?

anonymous · Answer

just 21

dumbcow · Answer

each bulb has probability of 0.995 of working
each bulb is independent
The combined probability of a string of bulbs working is the product of all the individual bulb probabilities.
0.995*0.995 is the probability that a string of 2 bulbs work and so on
$$0.995^{n} = 0.9$$
$$n = \frac{\log 0.9}{\log 0.995} = 21.02$$

anonymous · Answer

I can do this in my head ROFL you do not need all of that

anonymous · Answer

good job, dumbcow

dumbcow · Answer

no problem...you can divide logs in you head???

dumbcow · Answer

i dunno how else to do it

anonymous · Answer

I have to use caculator

anonymous · Answer

thank , can't do in my head , I'm slow

anonymous · Answer

OK so in my head i think of a black bord then i do the steps in my head small step by small step then when i am about to move on i take note of the # i am at, it helps a lot

I would not recommend this as you can do some stupid things xD but i think it is faster

anonymous · Answer

Gopeder was probably just pulling your leg. It's a little hard to believe that someone who has problems with 2 system equations can work out logarithmic equations in their head.
Also, the answer has to be round *up* to 22, not down to 21. As you already know, you can't have .02 lightbulbs.