Question

There are 52 playing cards in a standard deck. Each card is assigned to one of four suits: diamonds, hearts, spades or clubs. Within each suit, there are 13 ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. 1. Describe an outcome that is certain. Explain2. Suppose the card selected is assigned to the diamonds suit. Describe a different outcome that is equally likely.

Answer 1

Given:

Number of cards in a standard deck = 52

Each card is assigned to one of four suits: Diamonds, hearts, spades, or clubs

Number of Ranks in each suit = 13

Let's answer the folowing questions using the given information.

1) Describe an outcome that is certain.

An outcome can be said to be all possible results from an experiment.

A certain outcome is any possible outcome of the experiment. If the experiment is "that you draw a card and register its rank"

Then, for example, "the card drawn is an ace" is a certain outcome of the experiment.

Certain outcome: {the card drawn is an ace}

2) Suppose the card is assigned to the diamonds suit. Describe a different outcome that is equally likely.

If a card selected is assigned to diamonds suit, a different outcome that is equally likely is also if a card selected from any of the three other suits. This is because all cards are equally distributed in each of the four suits.

An outcome that is equally likely must have the same probability.

Thus, we can say suppose a card is assigned to the diamonds suit a different outcome that is equally likely is when a card selected is assigned to the spades suit.

We have the probablities of each event:

`\begin{gathered} P(\text{diamonds suit)=}(13)/(52) \\ \\ P(\text{spades suit)= }(13)/(52) \end{gathered}`