A student experiences difficulty with malfunctioning alarm clocks. Instead of using one alarm clock, he decides to use three. What is the probability that at least one alarm clock works correctly if each individual alarm clock has a 90% chance of working correctly?

Question

Is the answer as simple as 0.9^3 or is there more to it?

Answer 1

Or do you do the probability of the clocks not working?
0.1^3=0.001 then subtract from 1 to get the chances of at least 1 working
1-0.001= 0.999.

Answer 2

You're right.

Probability of an individual clock working properly = 0.9

Probability of an individual clock not working properly = 1 - 0.9 = 0.1

The probability of all three clocks not working properly = ( 0.1 )³ = 0.001

The probability that at least one clock is working properly = 1 - 0.001 = 0.999







Therefore the proabability that at least one clock is working properly

= 1 - 0.001