Probability Practice Test 2

Concept:Since an athlete can receive at most one medal in an event, getting gold, silver, and bronze are mutually exclusive events.Explanation:Let $G$, $S$, and $B$ be the events of getting gold, silver, and bronze respectively.Given:$P(G)=\frac{1}{20}$$P(S)=\frac{3}{10}$$P(B)=\frac{4}{7}$Because these events are mutually exclusive,$$P(\text{getting a medal})=P(G)+P(S)+P(B)$$$$=\frac{1}{20}+\frac{3}{10}+\frac{4}{7}$$Using LCM $140$,$$=\frac{7}{140}+\frac{42}{140}+\frac{80}{140}$$$$=\frac{129}{140}$$Therefore, probability of not getting any medal is$$P(\text{no medal})=1-P(\text{medal})$$$$=1-\frac{129}{140}$$$$=\frac{11}{140}$$This value is not present in the given options.Answer:$\frac{11}{140}$, so the correct choice is None of these.