question_answer

A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1, 2, 3,..., 8 (Fig. 9), which are equally likely outcomes. What is the probability that the arrow will point at (i) an odd number, (ii) a number greater than 3, (iii) a number less than 9.

Answer:

Total no. of outcomes \[=8\]

(i) Let \[{{E}_{1}}\] be the event or getting an odd number

\[\therefore \] Favourable outcomes \[=1,3,5,7\]

\[\Rightarrow \] No. of favourable outcomes \[=4\]

\[\therefore P({{E}_{1}})=\frac{4}{8}=\frac{1}{2}\]

(ii) Let \[{{E}_{2}}\] be the event of getting a number greater than 3.

\[\therefore \] Favourable outcomes \[=4,5,6,7,8\]

\[\Rightarrow \] No. of favourable outcomes \[=5\]

\[\therefore P({{E}_{2}})=\frac{5}{8}\]

(iii) Let \[{{E}_{3}}\]be the event of getting a number less than 9.

\[\therefore \] Favourable outcomes \[=1,2,3,4,5,6,7,8\]

\[\Rightarrow \] No. of favourable outcomes \[=8\]

\[\therefore P({{E}_{3}})=\frac{8}{8}=1\]