Class 11 Math Algebra Probability

An experiment involves rolling a pair of dice and recording the numbers that come up describe the following events:

A : the sum is greater than $8$

B : $2$ occurs on either die

C : the sum is at least $7$ and a multiple of $3$

Which pairs of these events are mutually exclusive?

A : the sum is greater than $8$

B : $2$ occurs on either die

C : the sum is at least $7$ and a multiple of $3$

Which pairs of these events are mutually exclusive?

Solution: When a pair of dice is rolled, the sample space will have $36$ sample points

$S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)(2,1),(2,2),...........,(2,6)(3,1),(3,2)..............(3,6)(4,1),(4,2).............(4,6),(5,1),(5,2).............(5,6)(6,1),(6,2)...........(6,6)}$

$A={(3,6),(6,3),(4,5),(5,4),(5,5),(4,6),(6,4),(5,6),(6,5),(6,6)}$

$B={(1,2),(2,1),(2,3),(3,2),(2,4),(4,2),(2,5),(5,2),(2,6),(6,2)}$

$C={(4,5),(5,4),(3,6),(6,3),(6,6)}$

Clearly, $A∩B=ϕ$

Hence, $A$ and $B$ are mutually exclusive events.

$B∩C=ϕ$

Hence, $B$ and $C$ are mutually exclusive events.

$A∩C={(4,5),(5,4),(3,6),(6,3),(6,6)}=ϕ$

Hence, $A$ and $C$ are not mutually exclusive events

$S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)(2,1),(2,2),...........,(2,6)(3,1),(3,2)..............(3,6)(4,1),(4,2).............(4,6),(5,1),(5,2).............(5,6)(6,1),(6,2)...........(6,6)}$

$A={(3,6),(6,3),(4,5),(5,4),(5,5),(4,6),(6,4),(5,6),(6,5),(6,6)}$

$B={(1,2),(2,1),(2,3),(3,2),(2,4),(4,2),(2,5),(5,2),(2,6),(6,2)}$

$C={(4,5),(5,4),(3,6),(6,3),(6,6)}$

Clearly, $A∩B=ϕ$

Hence, $A$ and $B$ are mutually exclusive events.

$B∩C=ϕ$

Hence, $B$ and $C$ are mutually exclusive events.

$A∩C={(4,5),(5,4),(3,6),(6,3),(6,6)}=ϕ$

Hence, $A$ and $C$ are not mutually exclusive events

Similar topics

determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

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