3. About 40% of all Waze-subscribed drivers will mark a speed trap ahead on their Waze app. Suppose seven cars have just driven past a police speed trap (and all seven drivers are waze subscribers). What is the probability at least one of the drivers will mark the speed trap on Waze? a. [C-4] What is a suitable probability distribution model in this case? Justify your choice. Use google-sheet file to construct probability distribution and histogram. Evaluate the expected number of these seven drivers who will mark the police speed trap on their app. What is the standard deviation? b. [T-4] Use proper notation and formula to evaluate the probabilities that (i) none of the seven drivers will mark the trap; (ii) fewer than three drivers will mark the trap. 4. A man buys a racehorse for $20 000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $100 000. If it wins one of the races, it will be worth $50 000. If it loses both races, it will be worth only $10 000. The man knows there's a 20% chance that the horse will win the first race and a 30% chance it will win the second one. Assume that the two races are independent events. a. [T-3] Develop a table for the discrete probability distribution in this case. b. [T-1] Determine the man's expected profit