When a normal, unbiased, 6-sided die is thrown, the numbers 1 to 6 are possible. These are the ONLY ‘events’ possible. This means these are EXHAUSTIVE as they cover ALL POSSIBLE OUTCOMES. The SUM of the probabilities of a set of EXHAUSTIVE EVENTS is ALWAYS 1

Taken together, are these events exhaustive or not? Throw a die and get an odd number Throw a die and get an even number {1, 3, 5} {2, 4, 6}

Taken together, are these events exhaustive or not? Get a 1 Get a number greater than 2 {1} {3, 4, 5, 6}

Taken together, are these events exhaustive or not? Throw a die and get a prime number Throw a die and get a composite number {2, 3, 5} {4, 6}

Event A: Probability of getting a 1 on a die = P(1) = 1 / 6 Event B: Probability of NOT getting a 1 on a die = P(1’) = 5 / 6 Event B is the COMPLIMENT of event A An event and its compliment are EXHAUSTIVE

Event A: Throw a die and get an EVEN NUMBER Event B: Throw a die and get an ODD NUMBER Events A and B CANNOT HAPPEN AT THE SAME TIME this means that events A and B are MUTUALLY EXCLUSIVE If two events, A and B, are MUTUALLY EXCLUSIVE then…

A coin is thrown and it lands on HEADS. It is thrown again. Is the probability of getting a head the 2 nd time greater, less or the same? The same coin is thrown 6 times and each time ends up as a head. If it is thrown for a 7 th time is the probability of getting ANOTHER head the 7 th time greater, less or the same this time?

If two events A and B are INDEPENDENT it means that if A happens then THIS DOES NOT AFFECT the probability of B occurring.

A B

A B The probability of A GIVEN THAT B has already happened.

If A and B are MUTUALLY EXCLUSIVE, P(A  B) = 0 If A and B are INDEPENDENT, P(A  B) = P(A) X P(B)

The events A and B are such that P(A) = 5 / 16, P(B) = ½, P(A|B) = ¼ Find (a)P(A  B)(2) (b)P(B’ | A)(3) (c)P(A’  B)(2) (d)Determine, with a reason, whether or not events A and B are independent (3)

The events A and B are such that P(A) = 5 / 16, P(B) = ½, P(A|B) = ¼ Find (a)P(A  B)(2)

The events A and B are such that P(A) = 5 / 16, P(B) = ½, P(A|B) = ¼ Find (b) P(B’ | A)(3) A B

The events A and B are such that P(A) = 5 / 16, P(B) = ½, P(A|B) = ¼ Find (c) P(A’  B)(2)

The events A and B are such that P(A) = 5 / 16, P(B) = ½, P(A|B) = ¼ Find (d) Determine, with a reason, whether or not events A and B are independent (3) If A and B are independent then P(A  B) = P(A) X P(B)

The events A and B are such that P(A) = 0.2 and P(A  B) = 0.6 Find (a)P(A’  B’)(2) (b)P(A’  B)(2) Given also that events A and B are independent, find (c)P(B)(4) (d)P(A’  B’) (2)

A B The events A and B are such that P(A) = 0.2 and P(A  B) = 0.6 Find (a)P(A’  B’)(2)

The events A and B are such that P(A) = 0.2 and P(A  B) = 0.6 Find (b) P(A’  B)(2) A BAB

The events A and B are such that P(A) = 0.2 and P(A  B) = 0.6 Find Given also that events A and B are independent, find (c)P(B)(4)

The events A and B are such that P(A) = 0.2 and P(A  B) = 0.6 Find Given also that events A and B are independent, find (d) P(A’  B’) (2)