Question

Submit teFor the experiment of drawing a single card from a standard 52-card deck, find (a) the probability, and (b) the odds in favor, that you do not draw a nine.(a) The probability(Type an integer or a simpified fraction.)(b) The odds i favor of not a nine are

Answer 1

QUESTION A

The probability of an event is calculated using the formula:

`P(E)=\frac{Number\text{ }of\text{ }favorable\text{ }outcomes}{Number\text{ }of\text{ }possible\text{ }outcomes}`

There are 4 nines in a standard deck of cards. Therefore, there are 48 cards that are not nines.

Since there are 52 cards, the probability is calculated to be:

`\begin{gathered} P=(48)/(52) \\ P=(12)/(13) \end{gathered}`

The probability is 12/13.

QUESTION B

Odds in favor of a particular event are given by the number of favorable outcomes to the number of unfavorable outcomes. The formula is written out to be:

`P(E)=\frac{Number\text{ }of\text{ }favorable\text{ }outcomes}{Number\text{ }of\text{ }unfavorable\text{ }outcomes}`

Since we have that the number of favorable outcomes is 48 and the number of unfavorable outcomes is 4, we have that the odds in favor are given to be:

`P=(48)/(4)=(12)/(1)`

The odds are 12 to 1.