Be sure to fully justify your responses when appropriate! Show where all your numbers came from if not explicitly written. Don't forget Units and use complete sentences when appropriate/asked for. 1. [10 pts] We bought a pack of 10 lightbulbs from a garage sale and 6 of them don't work. If we were to collect a random sample of 2 lightbulbs (no replacement) and count the number of lightbulbs that are defective, create a probability distribution for this discrete random variable. a) First, define your random variable 'X' The random variable 'X' will be defined as the number of defective lightbulbs in a random sample of 2 lightbulbs chosen without replacement from the pack of 10 bulbs. X can take from values 0 to 2, where X=0 means both bulbs are working, X=1 means one bulbs is working, and X=2 means both bulbs are defective. b) Next, showing work for all of your probabilities in the space below, fill in the table below (round probabilities to 4 decimal places): X P(X)