SOLUTION: I need help with this problem please. Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice. The probability that Sa

Algebra ->  Expressions-with-variables -> SOLUTION: I need help with this problem please. Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice. The probability that Sa      Log On


   

Question 295889: I need help with this problem please.
Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice.
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 probability 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!
Let x = probability that San Francisco will play in the next Super Bowl.
Let y = probability that San Francisco will not play in the next Super Bowl.

The probability that San Francisco will play in the next Super Bowl is 9 times the probability that they won't plan in the next Super Bowl.

This means the x = 9*y

You also know that probability that San Francisco will play in the next Super Bowl plus the probability that San Francisco will not play in the next Super Bowl is equal to 1.

This means that x + y = 1

Since x = 9*y, you can substitute in this equation to get:

9*y + y = 1

Combine like terms to get 10*y = 1

Divide both sides of this equation to get y = .1

Since x = 9 * y, this means that x = 9 * .1 = .9

You get x = .9 and y = .1

This means that the probability that San Francisco will play in the next Super Bowl is .9 and the probability that San Francisco will not play in the next Super Bowl is .1.

.9 is 9 * .1.
.9 + .1 = 1