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