Answer
47:5
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 = $\frac{P(not E)}{P(E)}$
We find the odds against drawing a club greater than 4 and less than 10.
E: {5,6,7,8,9 of clubs}
P(E) = $\frac{5}{52}$
P(not E) = 1 - P(E)
= 1 - $\frac{5}{52}$
=$\frac{52-5}{52}$ = $\frac{47}{52}$
Odds against E = $\frac{\frac{47}{52}}{\frac{5}{52}}$ = $\frac{47}{5}$
