Question

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as(i) number greater than 4(ii) six appears on at least one die Select the correct answer from above options

Answer 1

Here, the total number of outcomes,n(S)=62=36

(i) Number of outcomes when both tosses of die do not have a number greater than 4,(X=0)=4∗4=16

Number of outcomes when exactly one toss of die has a number greater than 4,(X=1)=4∗2+2∗4=16

Number of outcomes when both tosses of die have a number greater than 4(X=2),=2∗2=4

So, P(X=0)=

16

36

=

4

9

P(X=1)=

16

36

=

4

9

P(X=2)=

4

36

=

1

9

(ii) Number of outcomes when six does not appear on both tosses of die,(X=0)=5∗5=25

Number of outcomes when six appear only on one toss of die,(X=1)=5∗1+1∗5=10

Number of outcomes when six appear on both tosses of die,4(X=2),=1∗1=4

So, P(X=0)=

25

36

P(X=1)=

10

36

=

5

18

P(X=2)=

1

36

=

1

36