# MDM4U – Grade 12 Data Management – Probability Test

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.

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.