Questions: A board game uses the deck of 20 cards shown to the right. If one card is drawn, determine the probability that the card shows a yellow bird or a 4. The probability of selecting a yellow bird or a 4 is

Solution Steps

To determine the probability of drawing a card that shows a yellow bird or a 4, we need to count the number of cards that meet either of these criteria and then divide by the total number of cards.

1. Count the number of cards that show a yellow bird.
2. Count the number of cards that show a 4.
3. Subtract the number of cards that show both a yellow bird and a 4 (if any) to avoid double-counting.
4. Divide the result by the total number of cards to get the probability.

The total number of cards in the deck is given as \( 20 \).

There is \( 1 \) card that shows a yellow bird.

There are \( 4 \) cards that show a \( 4 \).

There are no cards that show both a yellow bird and a \( 4 \), so \( 0 \) cards fall into this category.

The total number of favorable outcomes is calculated as: \[ \text{Favorable Outcomes} = \text{Yellow Bird Cards} + \text{Cards with 4} - \text{Yellow Bird and 4} \] Substituting the values: \[ \text{Favorable Outcomes} = 1 + 4 - 0 = 5 \]

The probability \( P \) of drawing a card that shows a yellow bird or a \( 4 \) is given by: \[ P = \frac{\text{Favorable Outcomes}}{\text{Total Cards}} = \frac{5}{20} = \frac{1}{4} \]

Final Answer