Questions: Question 5 A single card is drawn from a deck, what is the probability of drawing a 5 and a red? P(5 and red)=17 / 26 P(5 and red)=1 / 26 P(5 and red)=15 / 26 P(5 and red)=7 / 13

Question 5

A single card is drawn from a deck, what is the probability of drawing a 5 and a red?
P(5 and red)=17 / 26
P(5 and red)=1 / 26
P(5 and red)=15 / 26
P(5 and red)=7 / 13

Transcript text: Question 5 A single card is drawn from a deck, what is the probability of drawing a 5 and a red? $P(5$ and red$)=17 / 26$ $P(5$ and red$)=1 / 26$ $P(5$ and red$)=15 / 26$ $P(5$ and red$)=7 / 13$

Solution

Solution Steps

To find the probability of drawing a 5 and a red card from a standard deck of 52 cards, we need to determine how many cards meet both criteria. There are two red suits (hearts and diamonds), and each suit has one 5. Therefore, there are 2 red 5s in the deck. The probability is the number of favorable outcomes (red 5s) divided by the total number of cards.

Step 1: Determine the Total Number of Cards

A standard deck of cards contains 52 cards. This is the total number of possible outcomes when drawing a single card.

Step 2: Identify the Number of Favorable Outcomes

There are two red suits in a deck: hearts and diamonds. Each suit contains one card with the number 5. Therefore, there are 2 red 5s in the deck.

Step 3: Calculate the Probability

The probability of drawing a red 5 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. This can be expressed as: \[ P(\text{red 5}) = \frac{\text{Number of red 5s}}{\text{Total number of cards}} = \frac{2}{52} = 0.03846 \]

Final Answer

$\boxed{\frac{1}{26}}$

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