**Compute the probability of randomly selecting a spade or diamond. P(spade or diamond)****Compute the probability of randomly selecting a spade or diamond or heart. P(spade or diamond or heart)****Compute the probability of randomly selecting a king or club. P(king or club)**

This question aims to find the **probability** of different cards from a standard deck. Moreover, from the deck of **52 cards**, one card is randomly selected.

Apart from that, the above question is based on the concept of statistics. Probability is simply how likely something is to happen, for example, a heads or tails result after a coin flip. In the same way, when a card is randomly selected, what are the chances or the probability that it is, for example, a spade or diamond.

## Expert Answer

The standard card decks have four different suits and 52 cards as a total. The **four suits are heart, spades, diamonds, and clubs**, and these suits have **13 cards each**. The standard equation of probability is as follows:

\[ P ( A ) = \dfrac{\text{Number of favorable outcomes of A}}{\text{Total number of outcomes}} \]

Therefore, the probability is calculated as follows:

**$P(\text{spade or diamond)}$**

\[ P(spade) = \dfrac{13}{52} \]

\[ P(spade) = \dfrac{1}{4} \]

\[ P(diamond) = \dfrac{13}{52} \]

\[ P(diamond) = \dfrac{1}{4} \]

So the probability of selecting a spade or a diamond is:

\[ \dfrac{1}{4} + \dfrac{1}{4} = \dfrac{1}{2} = 0.5 \]

**$P(\text{Spade or Diamond or Heart})$**

\[ P(heart) = \dfrac{13}{52} \]

\[ P(heart) = \dfrac{1}{4} \]

\[ P(spade) = \dfrac{13}{52} \]

\[ P(spade) = \dfrac{1}{4} \]

\[ P(diamond) = \dfrac{13}{52} \]

\[ P(diamond) = \dfrac{1}{4} \]

So the probability of selecting a spade, diamond or a heart is:

\[ \dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4} = \dfrac{3}{4} = 0.75 \]

**$P (\text{king or club) }$**

\[ P(club) = \dfrac{13}{52} \]

\[ P(club) = \dfrac{1}{4} \]

Each suite contains a king; therefore, there are four kings in a deck of cards.

So the probability of selecting a king is:

\[P(king) = \dfrac{4}{52}\]

\[P(king) = \dfrac{1}{13}\]

Moreover, there is a card that is the king of the club; therefore, the probability of it is as follows:

\[P(king of club) = \dfrac{1}{52}\]

Hence, the probability of randomly selecting king or club is:

\[P(king or club) = \dfrac{1}{4} + \dfrac{1}{13} – \dfrac{1}{52} = \dfrac{4}{13} = 0.308\]

## Numerical Results

The probability of selecting a number is as follows.

**$P(\text{spade or diamond)} = 0.5$**

**$P(\text{spade or diamond or heart)} = 0.75$**

**$P (\text{king or club) } = 0.308$**

## Example

Find the probability of rolling a 4 when a dice is rolled.

**Solution:**

As a dice has six different numbers, therefore, by using the probability formula given above, $P(4)$ is calculated as:

\[P(4) = \dfrac{4}{6}\]

\[= 0.667\]

*Images/ Mathematical drawings are created with Geogebra.*