Question

Question #99f41

Answer 1

`P(bar("Queen OR Jack")) =11/13`

Explanation:

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

`P("Queen of Hearts") = 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("Queen OR Jack") = 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(bar("Queen OR Jack")) = 52/52 - 8/52`

`P(bar("Queen OR Jack")) = 44/52`

`P(bar("Queen OR Jack")) = 11/13`

Answer 2

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.

`44/52 = (4 xx 11)/(4 xx 13) = (color(red)(cancel(color(black)(4))) xx 11)/(color(red)(cancel(color(black)(4))) xx 13) = 11/13`

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

`11/13 = 0.846`

`0.846 xx 100 = 84.6`

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