Question

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If two dice are rolled then the probability of getting the sum 5 is P(E1) , probability of getting it's sum 9 is P(E2) .
Verify that P(E1) = P(E2).
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Answer 1

we know that

probability= total number of favourable outcomes/total number of outcomes

according to question

the total number of event of when two dice rolled = 6^2 = 36

total number of favourable outcome= {(1,4),(4,1),(2,3),(3,2) }

p[E1] probability=4/36 = 1/9

favourable outcome of getting sum 9=

{(3,6),(6,3),(4,5),(5,4)}

p[E2] probability=4/36 = 1/9

so

p[E1] = p[E2] = 1/9

Hence proved

Answer 2

Answer:

Total outcomes= 6^2

=36

Favourable outcome = ( 1,4) ( 4,1) ( 3,2)(2,3)

Probablity= 4/36

=1/9

Now

For second case:-

Favourable outcomes = (3,6)(6,3)(5,4)(4,5)

Probability =4/36

=1/9

HENCE

P(1)=P(2)

Prove