Questions: 1.) When drawing a card from a deck that has 52 cards, what is the probability of getting a Red Card and a 7? 2.) When rolling a die, what is the chance of rolling a number greater than or equal to 3? 3.) A probability experiment is conducted which of these can AND can't be considered a probably outcome? Write yes or no beside the choice a). 100% b). 5/8 c). -0.48 d). 100.1% e.) 0

1.) When drawing a card from a deck that has 52 cards, what is the probability of getting a Red Card and a 7?
2.) When rolling a die, what is the chance of rolling a number greater than or equal to 3?
3.) A probability experiment is conducted which of these can AND can't be considered a probably outcome? Write yes or no beside the choice
a). 100%
b). 5/8
c). -0.48
d). 100.1%
e.) 0

Transcript text: 1.) When drawing a card from a deck that has 52 cards, what is the probability of getting a Red Card and a 7 ? 2.) When rolling a die, what is the chance of rolling a number greater than or equal to 3 ? 3.) A probability experiment is conducted which of these can AND can't be considered a probably outcome? Write yes or no beside the choice a). $100 \%$ b). $5 / 8$ c). -0.48 d). $100.1 \%$ e.) 0

Solution

Solution Steps

Solution Approach

To find the probability of drawing a red card and a 7 from a standard deck of 52 cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. There are two red 7s in a deck (7 of hearts and 7 of diamonds), and there are 52 cards in total.
To find the probability of rolling a number greater than or equal to 3 on a standard six-sided die, we count the number of favorable outcomes (3, 4, 5, 6) and divide by the total number of possible outcomes (6).
For each given probability value, determine if it is a valid probability. A valid probability must be between 0 and 1, inclusive.

Step 1: Calculate the Probability of Drawing a Red Card and a 7

To find the probability of drawing a red card and a 7 from a standard deck of 52 cards, we identify the number of favorable outcomes and divide it by the total number of possible outcomes. There are two red 7s in a deck (7 of hearts and 7 of diamonds). Therefore, the probability is:

\[ P(\text{Red and 7}) = \frac{2}{52} = 0.03846 \]

Step 2: Calculate the Probability of Rolling a Number Greater Than or Equal to 3

To find the probability of rolling a number greater than or equal to 3 on a standard six-sided die, we count the number of favorable outcomes (3, 4, 5, 6) and divide by the total number of possible outcomes (6). Thus, the probability is:

\[ P(\text{Number} \geq 3) = \frac{4}{6} = 0.6667 \]

Step 3: Determine Validity of Probability Outcomes

For each given probability value, we determine if it is a valid probability. A valid probability must be between 0 and 1, inclusive. The results are as follows:

$100\%$ is valid: $1.0$ is within the range $[0, 1]$.
$\frac{5}{8}$ is valid: $0.625$ is within the range $[0, 1]$.
$-0.48$ is not valid: it is less than 0.
$100.1\%$ is not valid: $1.001$ is greater than 1.
$0$ is valid: it is within the range $[0, 1]$.