Answer
9:10
Work Step by Step
The odds against E are found by taking the probability that E will not occur
and dividing by the probability that E will occur.
Odds against E = $\frac{P(not E)}{P(E)}$
Using the information given to us in the problem, we find the odds against selecting a tragedy or a history.
E: {10 history, 10 tragedy}
P(E)= $\frac{20}{38}$ = $\frac{10}{19}$
P(not E) = 1 - P(E)
= 1 - $\frac{10}{19}$
=$\frac{19 - 10}{19}$
= $\frac{9}{19}$
Odds against E = $\frac{\frac{9}{19}}{\frac{10}{19}}$ = $\frac{9}{10}$
