Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the...

Question:

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events:

R = red

B = black

A = ace

N = nine

D = diamond

C = club

a) Describe the sample space outcomes that correspond to each of these events.

b) For each of the following pairs of events, indicate whether the events are mutually exclusive. In each case, if you think the events are mutually exclusive, explain why the events have no common sample space outcomes. If you think the events are not mutually exclusive, list the sample space outcomes that are common to both events.

i) R and A

ii) R and C

iii) A and N

iv) N and C

v) D and C

Disjoint Events:

When two events are not Joint i.e. there is nothing which can be said common to both events. Disjoints are events are also called as Mutually exclusive events. Like, Event of drawing a King or Event of drawing a Queen. Both cannot occur together. So, they are mutually exclusive events.

Answer and Explanation:

a)

Corresponding sample space will be as follows:

R (red) :

There are 26 red cards which consist of diamond and heart suite.

B (black)

There are 26 black cards which consist of spade and club suite.

A (ace)

There are 4 ace, one from each suites.

N (nine)

There are 4 nine, one from each suites.

D (diamond)

There are 13 cards in 1 suite.

C (club)

There are 13 cards in 1 suite.

b)

i)

R and A are not mutually exclusive as red cards contain 2 aces

ii)

R and C are mutually exclusive as clubs are black cards not red cards.

iii)

A and N are mutually exclusive and there is no card which is both 9 and ace.

iv)

N and C are not mutually exclusive as there exists a club card which has 9 on it.

v)

D and C are mutually exclusive as diamond and club are different suite.


Learn more about this topic:

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Mutually Exclusive Events & Non-Mutually Exclusive Events

from 6th-8th Grade Math: Practice & Review

Chapter 48 / Lesson 5
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