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?
Is the answer as simple as 0.9^3 or is there more to it?
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.
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
To calculate the probability that at least one alarm clock works correctly, we need to consider the complementary probability, which means the probability that none of the alarm clocks work correctly.
The probability that a single alarm clock works correctly is 0.9. Therefore, the probability that a single alarm clock does not work correctly (i.e., fails) is 1 - 0.9 = 0.1.
Using this information, we can now calculate the probability that all three alarm clocks fail by multiplying the failure probabilities of each individual alarm clock:
0.1 * 0.1 * 0.1 = 0.001
This means that the probability that all three alarm clocks fail is 0.001.
Since we are interested in the probability that at least one alarm clock works correctly, the complementary probability will be:
1 - 0.001 = 0.999
Therefore, the probability that at least one alarm clock works correctly is 0.999, or approximately 99.9%.
To calculate the probability that at least one alarm clock works correctly, you need to consider the complementary probability. The complementary probability is the probability of the event not happening. In this case, it is the probability that none of the alarm clocks work correctly.
To find the probability that a single alarm clock does not work correctly, you subtract the probability of it working (90%) from 100%: 100% - 90% = 10%.
Since the three alarm clocks are independent, you can calculate the probability that all three do not work correctly by multiplying the individual probabilities together: 10% x 10% x 10% = 0.1^3 = 0.001.
Now, to find the probability that at least one alarm clock works correctly, you subtract the probability that none of them work from 100%: 100% - 0.001 = 99.9%.
So the probability that at least one alarm clock works correctly is approximately 99.9%.