Please show all work.

1. Among a group of 7 friends, 5 have a smart phone. Suppose we randomly pick two people from this group. First find the probability distribution function for this situation, where the random variable X represents the number of friends who have a smart phone. (Hint: start by drawing a probability tree). ii. Next, determine if this experiment is a binomial experiment by checking the conditions for a binomial experiment. a. Are there identical trials (repetitions)? b. Does each trial have two possible outcomes? If so, what did we call success and what did we call failure? c. Does the probability of success, denoted by p, remain the same in all trials? If so, what is the probability of success p? What is the probability of failure q? Does the random variable X denote the number of successes that occurs? e. Are the trials independent? f. Is the experiment in problem 6 a binomial experiment? That is, does it meet the requirements in a - e above