Question

Question #d1070

Answer 1

`"P(Jack)" = 1/13`

Explanation:

Question: "What is the probability of drawing the Jack of Hearts from the deck?"

Answer: `"P(Jack of Hearts)" = 1/52`

How did we obtain the probability?

We divide the number of successful outcomes, (1), by the number of all of the possible outcomes, (52).

Same question for Jack of Spades

Same answer: `"P(Jack of Spades)" = 1/52`

And so on for all 4 of the Jacks.

To expand the number of successful outcomes to all 4 Jacks we can add up the probabilities of each of the individual Jack:

`"P(Jack)" = "P(Jack of Hearts)" + "P(Jack of Spades)" + "P(Jack of Diamonds)" + "P(Jack of Clubs)"`

`"P(Jack)" = 1/52 + 1/52 + 1/52 + 1/52`

`"P(Jack)" = 4/52`

`"P(Jack)" = 1/13`

The more that we expand the number of successful outcomes (to perhaps Queens and Kings) the closer we get to `52/52 = 1` which means that it passes the test of being a true probability.