Question

The manager of an ice cream shop found that the probability of a new customer ordering vanilla ice is 7\9. What are the odds against a new customer ordering vanilla ice cream?

Answer 1

Answer:

The odds-against a new customer ordering a vanilla ice cream are: 2/7 or 2 to 7

Step-by-step explanation:

Odds-against is the ratio of probability of non-occurrence of an event to the probability of occurrence of an event.

Let p be the probability that the new customer will order vanilla

Then

$p = \frac{7}{9}$

Let q be the probability that the new customer will not order vanilla

$q = 1-p\\= 1 - \frac{7}{9}\\= \frac{9-7}{9}\\=\frac{2}{9}$

Now the odds against formula is:

$\frac{Probability\ of\ non-occurrence}{Probability\ of\ occurrence}= \frac{q}{p}\\=\frac{\frac{2}{9}}{\frac{7}{9}}\\=\frac{2}{9} * \frac{9}{7}\\=\frac{2}{7}$

Hence,

The odds-against a new customer ordering a vanilla ice cream are: 2/7 or 2 to 7