# Question 99f41

Nov 24, 2017

$P \left(\overline{\text{Queen OR Jack}}\right) = \frac{11}{13}$

#### Explanation:

The probability of drawing 1 specific card (e.g. Queen of Hearts) is:

$P \left(\text{Queen of Hearts}\right) = \frac{1}{52}$

That is 1 desired outcome divided by all of the possible outcomes, 52.

Wanting to draw a Queen or a Jack has 8 desired outcomes (4 Queens and 4 Jacks) divided by all of the possible outcomes, 52.

$P \left(\text{Queen OR Jack}\right) = \frac{8}{52}$

A fundamental principle of probability is that the probability all of the desired outcomes and the probability of all of the undesired outcomes must add up to 1.

P("Queen OR Jack") + P(bar("Queen OR Jack")) = 1

Note: the bar indicates NOT drawing a Queen or a Jack.

We can use this fact to find the probability of not drawing a Queen or Jack:

P(bar("Queen OR Jack")) = 1 - P("Queen OR Jack")#

$P \left(\overline{\text{Queen OR Jack}}\right) = \frac{52}{52} - \frac{8}{52}$

$P \left(\overline{\text{Queen OR Jack}}\right) = \frac{44}{52}$

$P \left(\overline{\text{Queen OR Jack}}\right) = \frac{11}{13}$

Nov 24, 2017

See a solution process below:

#### Explanation:

There are 8 cards you cannot get - 1 of 4 queens and 1 of 4 jacks.

Therefore there are $52 - 8 = 44$ cares you can get.

$\frac{44}{52} = \frac{4 \times 11}{4 \times 13} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 11}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 13} = \frac{11}{13}$

There is an 11/13 chance of getting something other than a queen or a jack.

$\frac{11}{13} = 0.846$

$0.846 \times 100 = 84.6$

There is an approximately 84.6% chance of getting neither a queen or a jack.