**Grade 12 – Data Management**

**Probability**

**Experimental and Theoretical Probability**

**Probability**: is the value between 0 and 1 that describes that likelihood of an occurrence of a certain event.**Experimental Probability:**making predictions based on a large number of previous results.**Theoretical Probability:**Make predictions based on a mathematical model.- In general, experimental probability will approach theoretical probability as the number of trials increase.
**Discrete Sample Space:**a sample space where you can count the number of outcomes ie. blue balls**Continuous Sample Space:**decimal numbers with infinite possibilities ie. Time.**Event:**is the occurrence of a specific outcome in the sample space.

P(A) = n(A) / n(S)

Probability of A is number of outcomes for A over total possibilities

**P(A’)**the probability that event A will not occur.- P(A’) = 1 – P(A)

**Odds**

**Odds:**a ratio used to represent a degree of confidence in whether or not an event will occur.**Odds In favour:**P(A) : P(A’)**= n(A) : n(A’)****Odds Against:**P(A’) : P(A)**= n(A’) : n(A)**

**Probability using counting principles**

- Instead of listing out all possibilities, counting principles such as combinations and permutations can be used to calculate all the possibilities of outcome and the possibilities of the event occurrence.
- Refer to these links for information about counting principles

**Independent and Dependent Event**

- Two events are independent if the occurrence of one event has no effect on the occurrence of another event.
- If two events are
**independent, then P (A n B) = P(A) P(B)** - Drawing tree diagrams with probability percentages on the branches can be multiplied
- P(AA) = P(A)*P(A)
- ie. When drawing disks from a bag, if the disks are replaced, the 2nd draw will be an independent event.
- ie. When drawing disks from a bag, but the disks are not replaced, the 2nd draw will be a dependent event.

**Mutually Exclusive Events**

- Two events are mutually exclusive if when one event occurs, the other event cannot occur.
- If two events are
**mutually exclusive, then P(A U B) = P(A) + P(B)** - If two events are
**not mutually exclusive, then P( A U B) = P(A) + P(B) – P(A U B)** - ie Probability of picking a KING or a FOUR is a mutually exclusive event.
- ie Probability of picking a KING or a RED card is non-mutually exclusive.

**Conditional Probability**

- The probability that an event will occur given that another compatible event that already occurred.
- P(A / B) = P(A and B) / P(B)
- Probability of A given the occurrence of B is equal to the probability of A and B over the probability that B has occurred.
- ie. Probability of drawing a QUEEN if we know the chosen card is a face card is an example of conditional probability.