In a batch of 12 electric

Question

In a batch of 12 electric bulbs, 3 are defective. Two bulbs are selected
at random and put into 3 sockets in a room. The probability that the
room is illuminated is??

Answer 1

I'm not sure how you are putting 2 bulbs into 3 sockets, so we'll ignore that and assume that each bulb gets a socket.

 

The probability that the room is illuminated is the probability that both bulbs are not defective.

To find the probability of two events happening together, just multiply the probability of each event separately.  In this case, we figure out the probability that the first bulb worked and multiply it by the probability that the second bulb worked.

 

P(1st bulb) = 9/12 = 3/4 since 9 out of the twelve bulbs are not defective.

 

P(2nd bulb) = 8/11 since there are only 8 working bulbs to pick from the remaining 11 after picking that first bulb.

 

P(both) = 3/4 x 8/11 =24/44=6/11