Please use the game table above to find Kyle and Debbie's mixed strategy equilibria. 1. W = Probability Kyle goes to Craft Fair. (1-W) = Probability Kyle goes to Monster Trucks. 2. Use this information to find Kyle's optimal probability of going to the craft fair and monster trucks. Hint, what values of W and (1 - W) make Debbie indifferent to choosing either craft fair or monster trucks? Z = Probability Debbie goes to Craft Fair. (1 - Z) = Probability Debbie goes to Monster Trucks. Use this information to find Debbie's optimal probability of going to the craft fair and monster trucks. Hint, what values of Z and (1 - Z) make Kyle indifferent to choosing either craft fair or monster trucks?

Please see the pictures below. I need help with both questions please and thank you.

In an amusement arcade there is a horse race with horses coloured red, yellow and green. Only one player can play this game at any time and the outcomes of each race are independent of previous races. You can either bet 10p or 20p. If you bet 10p then each horse is equally likely to win. If you bet 20p the corresponding probabilities are 50%, 30% and 20%, respectively. Three times as many people bet 10p as do 20p. Given red wins, what is the probability it had been a 20p bet? 0.333 0.300 0.313 0.298

(QUEEN'S SECRET AND GENIES) In old days, there was a queen and she had a secret problem to solve. To get an answer to her secret problem, the queen bought one female and one male genie lamps. The probabilities that her secret problem can be solved by the male and female genies are 0.3 and 0.4 respectively. A Queen looking for divine help. Assume the queen keeps the genies independently away from each other with a fear that both could not harm her, what is the probability that the queen's secret problem is solved by at least one of the genies? Note: Please keep accuracy upto two decimal places.