Question

A game is played by drawing 4 cards from an ordinary deck and replacing each card after it is drawn. Find the probability that at least 1 ace is drawn.

Answer 1

`0.066`

Step-by-step explanation:

Here, we want to get the probability that at least 1 ace is drawn

There are 4 aces in a deck of cards

The total number of cards is 52

This means we have a total of 48 non-ace cards

The probability of picking at least an ace means that:

1 ace, 3 others

or 2 aces, 2 others

or

3 ace, 1 other

or

4 ace, no other

These are all the possible pickling combinations

The probability of picking an ace is the number of ace cards divided by the total number of cards which are 4/52 = 1/13

For non-ace cards, we have the probability as 48/52 = 12/13

We are going to add the combinations

We have that as follows:

`\begin{gathered} ((1)/(13)*(12)/(13)*(12)/(13)*(12)/(13))\text{ + (}(1)/(13)*(1)/(13)*(12)/(13)*(12)/(13))\text{ + (}(1)/(13)*(1)/(13)*(1)/(13)*(12)/(13)) \\ +\text{ (}(1)/(13)*(1)/(13)*(1)/(13)*(1)/(13)) \end{gathered}`

Finally, we simply the above so as to get a single fraction

We have that as follows:

`(1728)/(28561)+(144)/(28561)_{}+(12)/(28561)+(1)/(28561)=\text{ }(1885)/(28,561)\text{ = 0.066}`