Question

If x dcnotes the number of sixes in throwing two dice, find the expectation of x

Answer 1

Answer:

Here, X represents the number of sixes obtained when two dice are thrown simultaneously. Therefore, X can take the value of 0, 1, or 2.

∴P(X=0)=P(notgettingsixonanyofthedice)=

36

25

P(X=1)=P(sixonfirstdieandnosixonseconddie)+P(nosixonfirstdieandsixonseconddie)

=2(

6

1

×

6

5

)=

36

10

P(X=2)=P(sixonboththedice)=

36

1

Therefore, the required probability distribution is as follows.

Then, expectation of X=E(X)=∑X

i

P(X

i

)

=0×

36

25

+1×

36

10

+2×

36

1

=

3

1

=0.33