4. Each of the below problems involves a random process and an unknown probability p where 0

4. Each of the below problems involves a random process and an unknown probability p where 0 < p < 1. Use the information given to find p. Give exact answers. It is possible that p has more than one value on a given part, or that no value of p is possible. a. A friend has a spinner that lands on one of three possibilities: A, B, or C. You are told there is a 50% chance of landing on A, and p P(spinner lands on B). The friend also mentions that if you spin twice, the chance of getting both a B and a C in some order is U. [Note: The phrase 32 "in some order" means that the number 3/32 is the probability for both cases (B then C, C then B) combined, not the value for each case separately.] b. An unfair coin with p P(getting tails) has just sold at auction. The auction house mentions that when you flip the coin 8 times and record the number of heads, the variance of the heads count is 3. [WISE] c. An unfair coin with p P(getting heads) is to be flipped 7 times. You are told the chance of getting exactly 1 head is twice the chance of getting all tails. [WISE]