The chances that A&M will win this weekend\'s football game if they score less t

Question

The chances that A&M will win this weekend's football game if they score less than or equal to 20 points is 20%. Also, there is a 50% probability that they will win if they score between 20 and 40 points. However there is a 0.8 probability of winning the game if they score greater than or equal to 40 points. Given the team's record, strengths and the opponents, the probability that A&M will score less than or equal to 20 points is 0.5, between 20 and 40 points is 0.3, and, greater than or equal to 40 points is 0.2 only. What is the probability that A&M will win this weekend's game? If you did not watch the game and someone told you that A&M won, what is the probability they scored more than 40 points?

Can you use proper notation like:

P(AlB), P(A), 1-P(A), etc you know what I mean

Explanation / Answer

Chances that A&M will win this weekend's football game if they score less than or equal to 20 points is 20%.

There is a 50% probability that they will win if they score between 20 and 40 points.

There is a 0.8 probability of winning the game if they score greater than or equal to 40 point

the probability that A&M will score less than or equal to 20 points is 0.5, between 20 and 40 points is 0.3, and, greater than or equal to 40 points is 0.2 only.

The probability that A&M will win this weekend's game = P( wins if they scores <= 20)*P( score <=20) + P( wins if the scores are between 20 and 40)*P( score between 20 and 40) +P( wins if they scores >=40)*P( score >=40)

= .20*.5 + .50*.3 + .8*.2

= 0.41

If you did not watch the game and someone told you that A&M won, what is the probability they scored more than 40 points?

= P( they score more than 40 given they won)

=P( wins if they scores >=40)*P( score >=40) / P( wins)

= 0.8*.2/.41

= 0.39

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