Box 1 contains 1000 lightbulbs of which 10% are defective. Box 2 contains 2000 lightbulbs of which 5% are defective. (a) Suppose a box is given to you at random and you randomly select a lightbulb from the box. If that lightbulb is defective, what is the probability you chose Box 1? (b) Suppose now that a box is given to you at random and you randomly select two light - bulbs from the box. If both lightbulbs are defective, what is the probability that you chose from Box 1? 4 Solve the Rainbow

a) There is a 66.7% chance that you were given box 1

b) There is a 80% chance that you were given box 1

Step-by-step explanation:

To find this, we need to note that there is a 1/10 chance of getting a defective bulb with box 1 and a 1/20 chance in box 2.

a) To find the answer to this, find the probability of getting a defective bulb for each box. Since there is only one bulb pulled in this example, we just use the base numbers given.

Box 1 = 1/10

Box 2 = 1/2

From this we can see that Box 1 is twice as likely that you get a defective bulb. As a result, the percentage chance would be 2/3 or 66.7%

b) For this answer, we need to square each of the probabilities in order to get the probability of getting a defective one twice.

Box 1 = 1/10^2 = 1/100

Box 2 = 1/20^2 = 1/400

As a result, Box 1 is four times more likely. This means that it would be a 4/5 chance and have a probability of 80%