Probability carries about 15 of the 150 marks in Paper 1. Most questions come down to a few rules and the fundamental counting principle, so learn when each one applies.
Question 1: Addition rule and independence
P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2. Find P(A or B) and test whether A and B are independent. P(A or B) = 0.5 + 0.4 − 0.2 = 0.7. Since P(A) × P(B) = 0.2 = P(A and B), they are independent. Answer: 0.7, and yes.
Question 2: Mutually exclusive events
A and B are mutually exclusive, with P(A) = 0.3 and P(B) = 0.5. Find P(A or B). Mutually exclusive events cannot happen together, so P(A and B) = 0. Answer: 0.8.
Question 3: Arranging digits
How many 5-digit codes can be made from the digits 1 to 5 with no digit repeated? There are 5 choices, then 4, 3, 2 and 1. Answer: 5! = 120.
Question 4: Arrangements and probability
The letters of MATRIC are arranged at random. What is the probability that the arrangement starts with M? There are 6! = 720 arrangements, and 5! = 120 start with M. Answer: 120/720 = 1/6.
Question 5: Repeated letters
How many different arrangements can be made from the letters of LEVEL? There are 5 letters, with L repeated twice and E repeated twice. Answer: 5! / (2! × 2!) = 30.
Question 6: Without replacement
A bag holds 3 red and 2 blue balls. Two are taken out without replacement. Find the probability that both are red. P = 3/5 × 2/4. Answer: 3/10. After the first ball, both the red count and the total go down by one.
Question 7: Complementary events
The probability of rain tomorrow is 0.35. Find the probability that it does not rain. Complementary events add up to 1, so P(no rain) = 1 − 0.35. Answer: 0.65.
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