A furniture factory makes a $4$-piece desk. Each piece is manufactured separately, and sets containing the $4$ pieces that make up the desk are then packaged together. Quality control at the factory has randomly sampled numerous desk sets and determined the number of damaged pieces in each set. The table below is a partially completed probability distribution for the random variable $X =$ the number of damaged pieces in a randomly selected desk set from this factory. | | | | | | - | - | - | - | - | - $x$| $0$ | $1$ | $2$ | $3$ | $4$ $p(x)$ | $0.75$ | $0.14$ | $0.07$ | $0.03$ | $?$ **What is the probability that a randomly selected desk set contains four damaged pieces?** [[☃ math-keypad 1]] **Write the event "desk contains at least two damaged pieces" in terms of $X$.** $P(X$ [[☃ dropdown 1]] [[☃ dropdown 2]]$)$ **What is the probability that a randomly selected desk set will contain at least two damaged pieces?** [[☃ math-keypad 2]]