Question

if two dice are rolled one time, write the sample space and find the probability of getting these results.

(a) A sum of 6 or 10 or 11.

(b) The product of the two outcomes in an even number.

(c) A sum less than or equal to 7.

(d) Face 2 on any dice.

(e) Prime number on both the dice.

(f) Even number on first dice and odd number on second dice

Answer 1

In every question A is a considered event

a) There are 5, 3, 2 possabilities of getting a sum of 6, 10, 11 respectively, so

$P(A)={\frac {5+3+2} {36}}={\frac 5 {18}}$

b) Product of outcome is an even number means at least one of the values is even, so

$P(A)=1-P(\neg A)=1-{\frac 1 2}*{\frac 1 2}={\frac 3 4}$

c) There are 0, 0, 1, 2, 3, 4, 5, 6 possabilities of getting a sum of 0, 1, 2, 3, 4, 5, 6, 7 respectively, so

$P(A)={\frac {0+0+1+2+3+4+5+6} {36}}={\frac {21} {36}}={\frac 7 {12}}$

d) $P(A)=1-P(\neg A)=1-({\frac 5 6})^2={\frac {11} {36}}$

e) Prime numbers is 2, 3, 5, so

$P(A)=({\frac 3 6})^2={\frac 1 4}$

f) There are 3 even and 3 odd numbers, so

$P(A)={\frac 3 6}*{\frac 3 6}={\frac 1 4}$