Help with basic Probability question

[MarcWhittle]

Hi, I need some help with this question for my nurses training, I have researched and simply can't find out how to do it. I don't want the answer, just an explanation how to solve it

The probability of a disposable thermometer being faulty is 10%. If a Nurse chooses three of these thermometers at random, what is the probability that none is faulty?

 

[Deleted member 4993]

Hi, I need some help with this question for my nurses training, I have researched and simply can't find out how to do it. I don't want the answer, just an explanation how to solve it

The probability of a disposable thermometer being faulty is 10%. If a Nurse chooses three of these thermometers at random, what is the probability that none is faulty?

First we assume that the nurse can make the choice from a group of many thermometers.

What is the probability that the first thermometer chosen is not faulty? → 1 - 0.1 = 0.9.

Choice of this "non-faulty" thermometer does not affect the probability of "faultiness" of the second thermometer? That remains 10% (=0.1). Now:

What is the probability that the second thermometer chosen is not faulty? → 1 - 0.1 = 0.9. These remain same (as the probability of picking a faulty thermometer). Now:

What is the probability that the first AND the second thermometer chosen - is not faulty? → = 0.9 * 0.9 = 0.81 (Why - tell us what does your textbook say). Now, following the same logic,:

What is the probability that the first AND the second AND the third thermometer chosen - is not faulty? = ??