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3. Consider the quadratic polynomial x2 + ax + b. If a and b are randomly selected to be positive integers which are less than or equal to 10. What is the probability that the polynomial is factorable over the integers?

4. A bag contains 3 red balls and 2 blue balls. Tom draws one ball in each hand. He looks at one hand and observes the color. What can he assume is the probability that the ball in his other hand is a different color?

 May 19, 2023
 #1
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3. The pairs (a,b) that work are (2,1), (3,2), (4,3), (4,4), (5,4), (6,3), (6,8), (7,6), (7,10), (8,7), (9,8), (10,9).  So the probability is 12/100 = 3/25.

 May 19, 2023
 #2
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4. The probability is 5/13.

 May 20, 2023
 #3
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how?

Guest May 20, 2023

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