A non-zero integer x is selected randomly from the set of integers x ∈ ℤ | - 25 ≤ x ≤ 25 , x ≠ 0 . The probability that x + 6 ≤ 135 x is

Step-by-step solution

x ∈ Z but x ≠ 0 where x ∈ Z - 25 ≤ x ≤ 25 Now, x + 6 ≤ 135 x   ⇒   x 2 + 6 x - 135 x ≤ 0 ⇒ x + 15 x - 9 x ≤ 0 The solution set is x ∈ ( - ∞ , - 15 ] ∪ ( 0 , 9 ] Given that x ∈ ℤ | - 25 ≤ x ≤ 25 , x ≠ 0 Common interval is x ∈ - 25 , - 15 ∪ ( 0 , 9 ] Total number of integers in ( 0 ,   9 ]   and - 25   , - 15 are 9 + 11 = 20   Total numbers in sample space, - 25 ≤