Cambridge International Mathematics

Suppose we select a card at random from a normal pack of 52 playing cards. Consider carefully these events:

Event X: the card is a heart Event Y: the card is an ace Event Z: the card is a 7

Notice that:

² XandYhave a common outcome: the Ace of hearts

² XandZhave a common outcome: the 7 of hearts

² YandZdo not have a common outcome.

When considering a situation like this:

² if two events have no common outcomes we say they aremutually exclusiveordisjoint

² if two events have common outcomes they arenot mutually exclusive.

Notice that: P(aceorseven)= 528 and P(ace)+P(seven)= 524 + 524 = 528

If two eventsAandBaremutually exclusivethen P(AorB)=P(A)+P(B)

Notice that: P(heartorseven)=^1652 and P(heart)+P(seven)=^1352 + 524 =^1752 :

Actually, P(heartorseven)=P(heart)+P(seven)¡P(heartandseven).

If two eventsAandBarenot mutually exclusivethen P(AorB)=P(A)+P(B)¡P(AandB).

EXERCISE 25J

1 An ordinary die with faces 1 , 2 , 3 , 4 , 5 and 6 is rolled once. Consider these events:

A: getting a 1 B: getting a 3 C: getting an odd number

D: getting an even number E: getting a prime number F: getting a result greater than 3.

a List all possible pairs of events which are mutually exclusive.

b Find: i P(BorD) ii P(DorE) iii P(AorE)

iv P(BorE) v P(CorD) vi P(AorBorF).

MUTUALLY EXCLUSIVE AND NON-MUTUALLY

EXCLUSIVE EVENTS [10.5]

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suit

value

C

D

H

S

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suit

value

C

D

H

S

Probability (Chapter 25) 527

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Y:\HAESE\IGCSE01\IG01_25\527IGCSE01_25.CDR Monday, 27 October 2008 2:31:38 PM PETER