posted by .

A building has three rooms. Each room has two separate electric lights. There are thus six Electric lights altogether. After a certain time there is a probability of 0.1 that a given light will have failed and all light are independent of all other lights. Find the probability that, after this time, there is at least one room in which both lights have failed

  • maths -

    Concentrate on a single room for a moment. It's got two bulbs, each of which has a 1/10 chance of failing, so at the end of the time interval in question the chance of a double failure is 1/10 x 1/10 = 1/100. It's only double failures we're interested in here, so we don't need to bother to work out the chance of a single failure or no failures, even though they're easy enough to work out. What we DO need to work out is the chances of this NOT happening - and that's just (1 - 1/100) = 99/100.

    Now look at all three rooms. We want to know the chances of there being AT LEAST ONE room in which both lights have failed - and that's just one minus the probability of all THREE rooms NOT having a double failure. But we know the probability of just one room not having a double failure, because we worked it out in the previous paragraph: it's 99/100. We know all failures are independent of one another, so the probability of all three rooms not having a double failure must be (99/100)^3, which is roughly 0.97. What do you think - does the logic hold together?

  • maths -

    Oops! Actually, we want one minus that, don't we. The chances of at least one room having a double failure is one minus the chances of none of them having a double failure - and that's 1 - 0.97, which is 0.03. That's more like it.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions


    THERE ARE 3 LIGHT HOUSES,THE FIRST ONE SHINE FOR 3 SECONDS, THEN IS OFF FOR 3 SECONDS.the 2 one shine for 4 seconds then is off for 4 seconds.the 3 one shine for 5 seconds,then is off for 5 seconds.all thr 3 lights have just come together.when …
  2. Math Prob/solving

    As Frank drives to work he has to pass through three lights. The probability that any light is green is 39%. Estimate the probability that exactly two lights will be green. Use the following list of digits which was taken from a table …
  3. Math

    The Lifetimes of a certain brand of photographic light are normally distributed with the mean of 210 h and a standard deviation of 50 h. What percent of lights will need to be replaced within 233 h?
  4. probability

    a teacher on her way to work passes through 3 stoplights each morning. the distances between the stop lights are great and the lights operate independently of each other. if the probability of the red lights are .4,.8 and .6 for each …
  5. math

    Marley drives to work every day and passes two independently operated traffic lights. The probability that both lights are red is 0.35. The probability that the first light is red is 0.48. What is the probability that the second light …
  6. statistic

    A student must pass through 12 sets of traffic lights on his way to university. Suppose that each of the lights is green 39.5% of the time, yellow 5.9% of the time, and red 54.6% of the time. Suppose also that the traffic lights function …
  7. Finite Math

    A box contains two defective Christmas tree lights that have been inadvertently mixed with eight nondefective lights. If the lights are selected one at a time without replacement and tested until both defective lights are found, what …
  8. English

    What can you do to save electricity? 1. I can turn off the lights when I leave my room. 2 I can turn off the lights when I don't use the room. 3.I can turn off the lights when I don't stay in the room. 4. I can turn off the lights
  9. statistics

    24. Suppose there are five traffic lights that you need to pass while driving from your work to school. The probabilities that you will stop for these red lights are: 0 red light with probability 0.05, 1 red light with probability …
  10. math

    Ms. Tucker travels through two intersections with traffic lights as she drives to the market. The traffic lights operate independently. The probability that both lights will be red when she reaches them is .22. the probability that …

More Similar Questions