need work please show ALL WORK due by thru10am asap

1. You pay $5 to play a game. There is a 10% chance you will win $5, a 40% chance you will win $7 and a 50% chance you will win $3. a. Calculate the expected value, variance, and standard deviation of the game b. Is it statistically favorable to play the game? Justify your answer. (Yes or no answers will NOT receive full credit!) 2. A commuter must pass through five traffic lights on the way to work. They estimate the probability model for the number of red lights they hit as follows. x = # of red lights 0 1 2 3 4 5 P(x) 0.05 0.25 0.35 0.15 0.15 0.05 a. Is this a valid probability distribution? Why or why not? b. What is the probability that our commuter hits at least 4 red lights on the way to work? c. What is the probability that our commuter hits at most 2 red lights on the way to work? d. How many red lights should they expect to hit? e. What is the variance and standard deviation of the number of red lights the commuter will hit? 3. A local pet shelter has the following distribution of pets. Male Female Dog 8 16 Cat 6 12 a. What is the probability that a randomly selected pet is male? b. What is the probability that a randomly selected pet is female or a dog? c. What is the probability that a randomly selected pet is a male cat? d. What is the probability that a randomly selected pet is a dog given that it is male? 4. You flip a coin and roll a six sided die. a. List the sample space b. What is the probability of flipping a heads or rolling less than a 4? c. What is the probability of flipping a heads and rolling a 6? d. What is the probability of flipping a tails and rolling a 2 or flipping tails and rolling a 3? e. What is the probability of rolling at least a 5 given that you’ve flipped heads?