Key Problem Solving Steps
Clearly state the total number of possible outcomes N.
Count the exact number of favorable outcomes m that satisfy the condition.
Calculate P(E) = m / N and simplify to lowest terms fraction.
Step-by-Step Problem Solving
12 defective pens are accidentally mixed with 132 good ones. One pen is taken out at random. Find the probability that the pen taken out is a good one.
Defective pens = 12, Good pens = 132.
Total possible outcomes = 12 + 132 = 144.
Favorable outcomes (good pens) = 132.
A box contains 90 discs numbered 1 to 90. If one disc is drawn at random, find the probability that it bears: (i) a two-digit number, (ii) a perfect square number.
Total possible outcomes = 90.
(i) A Two-Digit Number:
1-digit numbers are 1 to 9 (9 numbers). Two-digit numbers are 10 to 90 ⟹ Favorable outcomes = 90 - 9 = 81.
(ii) A Perfect Square Number:
Perfect squares between 1 and 90 are: 1, 4, 9, 16, 25, 36, 49, 64, 81 ⟹ Favorable outcomes = 9.
Key Takeaways
Always verify the total number of outcomes before writing fractions.
Reduce fractions to their simplest form for full board exam marks.
For 'NOT E' questions, use P(NOT E) = 1 - P(E) for fast calculation.