Question

If two dice are rolled what is the probability of the sum is less than 10

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Two dice are rolled}$

$\underline{\textbf{To find:}}$

$\textsf{The probability of the sum is less than 10}$

$\underline{\textbf{Solution:}}$

$\textsf{When two dice are rolled,}$

$\mathsf{Sample\;space\,S=}\left\{\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\end{array}\right\}$

$\implies\mathsf{n(S)=36}$

$\textsf{Let A be the event of getting sum less than 10}$

$\mathsf{A=}\left\{\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&\\(5,1)&(5,2)&(5,3)&(5,4)&&\\(6,1)&(6,2)&(6,3)&&&\end{array}\right\}$

$\implies\mathsf{n(A)=30}$

$\mathsf{Now,}$

$\mathsf{Probability\;of\;A=\dfrac{Number\;of\;ways\;favourable\;to\;the\;event\;A}{Total\;number\;of\;ways}}$

$\mathsf{P(A)=\dfrac{n(A)}{n(S)}}$

$\mathsf{P(A)=\dfrac{30}{36}}$

$\implies\boxed{\mathsf{P(A)=\dfrac{5}{6}}}$

Answer 2

Answer:

Step-by-step explanation: