Questions & Answers

Question

Answers

Answer

Verified

130.5k+ views

* Probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.

Find the total outcomes.

We have a total of $52$ cards in a well-shuffled deck.

$\therefore $ Total outcomes $ = 52.$

Find the favorable outcomes.

There are $4$ ace cards in a deck of $52$ cards.

$\therefore $ Total non-ace cards $ = 52 - 4 = 48.$

$\therefore $ Total favorable outcomes $ = 48.$

Find the probability that the card will not be an ace by using a probability formula.

Probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.

Probability ${\text{ = }}\dfrac{{{\text{48}}}}{{{\text{52}}}}$

Cancelling out common factors from numerator and denominator.

$ = \dfrac{{12}}{{13}}$

$\therefore $ Probability that the card will not be an ace $ = \dfrac{{12}}{{13}}$.

Alternate method:

Probability that the card will not be an ace $ = 1 - $ Probability that the card will be an ace

There are $4$ ace cards in a deck of $52$ cards.

Probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.

Probability $ = \dfrac{4}{{52}}$.

Probability that the card will not be an ace $ = 1 - $ Probability that the card will be an ace

$

= 1 - \dfrac{4}{{52}} \\

= \dfrac{{52 - 4}}{{52}} \\

= \dfrac{{48}}{{52}} \\

= \dfrac{{12}}{{13}} \\

$

Probability that the card will not be an ace $ = \dfrac{{12}}{{13}}$.