A box of 80 candles consists of 30 defective and 50 non defective candles. If10 of these candles are selected at random, what is the probability?
a) All will be defective.
b) 6 will be non defective
c) All will be non defective
�
The total number of candles = 80
The number of defective candles = 30
The number of non-defective candles = 50
a) Probability of all candles selected at random being defective:
To calculate this probability, we can use the formula for probability: (number of favorable outcomes) / (total number of possible outcomes).
In this case, the number of favorable outcomes is 0 because there are not enough defective candles to choose from to select 10 defective candles. Therefore, the probability is 0.
b) Probability of 6 candles being non-defective:
To calculate this probability, we can use the formula for probability: (number of favorable outcomes) / (total number of possible outcomes).
The number of favorable outcomes can be calculated using combinations, as we want to choose 6 non-defective candles out of 50 non-defective candles:
Favorable outcomes = C(50, 6)
The total number of possible outcomes is the number of ways to choose any 10 candles out of 80 candles:
Possible outcomes = C(80, 10)
Using these values, we can calculate the probability as:
Probability = (number of favorable outcomes) / (total number of possible outcomes)
c) Probability of all candles being non-defective:
To calculate this probability, we can use the formula for probability: (number of favorable outcomes) / (total number of possible outcomes).
The number of favorable outcomes is 1 because there is only one way to choose 10 non-defective candles, which is to choose all the 50 non-defective candles. Therefore, the probability is 1.
Hope this helps! Let me know if you have any other questions.