Siko is a contestant on a TV game show called Win a Million. Each time

Question

she answers a multiple-choice question correctly, she wins money. If she picks a wrong answer, she is eliminated. If Siko does not know the right answer, she can use one of the following Helping Hands:
• Quiz the Crowd: She can poll the audience. The crowd has an experimental probability of being correct 85% of the time.
• Double Up: She can give two answers, instead of just one. If either is correct she stays in the game.
• Rule One Out: One of the incorrect answers is removed, leaving three choices.
Suppose Siko encounters three questions in a row to which she does not know the answers.
a) Assuming that she can use each Helping Hand only once during the game, and only once per question, what is the best estimated probability Siko has of staying
alive through the three questions? What assumptions did you make.
b) How many more times is Siko likely to stay in the game if she uses all three Helping Hands than if she simply guesses at random on all three questions?