# Combined events for OCR GCSE Maths 1. Combined events
2. Independent combined events
3. Dependent combined events
4. Tree diagrams

Systematic listing is when all possible outcomes of combined events are listed so that none are missed out. This can then be used to calculate the probability of any event happening. The product rule for counting states that multiplying the number of possible outcomes for each event together gives the total number of outcomes for combined events. The probability of independent combined events can be found by multiplying the probabilities of the individual events. If the first event that occurs affects the probability of the second event occuring, then the two events are dependent. Probabilities can be calculated by multiplying the individual probabilities together. Tree diagrams show different combinations of events and the probabilities of each event occuring. To find the probability of a specific combination occuring, the probabilities of the individual events are multiplied together. If the probability of the first event occuring does not affect the probability of the second one occuring, the two events are independent. # 1

A deck of 52 cards is made up of equal red and black cards. Two cards are drawn without replacement. State how the given tree diagram shows that the events are dependent.

The probability for the same outcome changes on the tree diagram after the first card is drawn, therefore the events are dependent. # 2

An A-Level student can pick between 12 classes to take. The student can choose 3 classes. Calculate how many combinations of the classes the student can take.

Total number of combinations = 12 × 11 × 10 = 1320. # 3

List all the possible ways in which a three-digit number can be made using the following digits, given that each digit is used once: 1, 2, 3.

The possible outcomes are: 123, 132, 213, 231, 312, 321. # 4

Anna keeps 8 pairs of shorts and 12 T-shirts in the same drawer. She draws two random items from a drawer. Calculate the probability that she gets a T-shirt and a pair of shorts.

P(T-shirt and shorts) = 8/20 × 12/19 + 12/20 × 8/19 = 48/95. # 5

Two cards are drawn, with replacement, out of an ordinary deck. Calculate the probability that the first card is an 8 and the second card is red.

P(first is 8 and second is red) = 4/52 × 26/52 = 1/26. End of page