Question

2, 3, and 5 are substituted at random for a, b, and c in the equation ax+b=c. Probability that solution is negative? P( absolute value = 1?

Answer 1

ok, well you can brute force this

Answer 2

if assignment is random, then the probability of something is always (number of success possibilities)/ (total number of possibilities)

Answer 3

so there are a total of six possibilities and we can actually list them all:

Answer 4

hmmm actually ok misread, there is an x variable haha

Answer 5

ok so let's list the six possibilities anyway and see where that gets us

Answer 6

1. 2x + 3 = 5
2. 2x + 5 = 3
3. 3x + 5 = 2
4. 3x + 2 = 5
5. 5x + 3 = 2
6. 5x + 2 = 3

Answer 7

k. im with you so far

Answer 8

ok cool, so now let's solve the cases

Answer 9

1. 2x = 2. x = 1 (not negative)

Answer 10

2. 2x = -2. x = -1 (negative)

Answer 11

3. 3x = -3. x = -1. (negative)

Answer 12

4. 3x = 3. x = 1. (positive)

Answer 13

5. 5x = -1. x = -1/5. (negative)

Answer 14

6. 5x = 1. x = 1/5 (positive)

Answer 15

so out of the six possibilities, 3 are positive, 3 are negative

Answer 16

so thats a 50 percent probabilty

Answer 17

exactly

Answer 18

and sometimes there's no systematic theorem or rule - it's just #outcomes/#possible outcomes

Answer 19

right.