SOLUTION: Write a system of two equations in two unknowns. The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Sup

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Question 259715: Write a system of two equations in two unknowns. The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probablity that they do not play is 1. What is the probability that San Francisco plays in the next Super Bowl?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
probability that they play is 9 times the probability that they don't.

let p(y) = probability that they play.

let p(n) = probability that they don't play.

p(y) = 9 * p(n)

the probability that they play plus the probability that they don't play must equal 1 since these options are mutually exclusive and there are no other options.

you get:

p(y) + p(n) = 1

now:
p(y) = 9 * p(n), so this equation is equivalent to:

9*p(n) + p(n) = 1

this means that 10*p(n) = 1

this means that p(n) = 1/10 = .1

this means that p(y) = 9 * p(n) = 9 * .1 = .9

p(y) = .9
p(n) = .1

the probability that san francisco plays in the next super bowl is .9 * 100% = 90%.