Questions: One card is drawn from an ordinary deck of 52 cards. Find the probabilities of drawing the following cards. a. A 5 or 9 b. A red card or an 8 c. A 9 or a black 8 d. A diamond or a black card e. A face card or a heart

Solution Steps

To solve these probability questions, we need to understand the composition of a standard deck of 52 cards and use basic probability principles.

• There are 4 fives and 4 nines in a deck.
• Total favorable outcomes = 4 (fives) + 4 (nines) = 8.

• There are 26 red cards in a deck.
• There are 4 eights in a deck, 2 of which are red.
• Total favorable outcomes = 26 (red cards) + 2 (black eights) = 28.

• There are 4 nines in a deck.
• There are 2 black eights in a deck.
• Total favorable outcomes = 4 (nines) + 2 (black eights) = 6.

To find the probability of drawing a 5 or a 9 from a standard deck of 52 cards, we calculate the total number of favorable outcomes. There are 4 fives and 4 nines, giving us:

\[ \text{Total favorable outcomes} = 4 + 4 = 8 \]

Thus, the probability \( P(A) \) is given by:

\[ P(A) = \frac{\text{Total favorable outcomes}}{\text{Total cards}} = \frac{8}{52} \approx 0.1538 \]

Next, we calculate the probability of drawing a red card or an 8. There are 26 red cards in the deck and 4 eights, of which 2 are red. Therefore, the total number of favorable outcomes is:

\[ \text{Total favorable outcomes} = 26 + (4 - 2) = 28 \]

The probability \( P(B) \) is then:

\[ P(B) = \frac{28}{52} \approx 0.5385 \]

Finally, we find the probability of drawing a 9 or a black 8. There are 4 nines and 2 black eights in the deck, leading to:

\[ \text{Total favorable outcomes} = 4 + 2 = 6 \]

Thus, the probability \( P(C) \) is:

\[ P(C) = \frac{6}{52} \approx 0.1154 \]

Final Answer