Math / Data & Statistics

QuestionA standard die is rolled. Find the probability that the number rolled is less than 5. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer

Studdy Solution

STEP 1

What is this asking? What are the chances of rolling a number smaller than 5 on a regular six-sided die? Watch out! Don't include 5 itself; we only want numbers less than 5!

STEP 2

1. List the possible outcomes
2. List the favorable outcomes
3. Calculate the probability

STEP 3

When we roll a standard die, the possible outcomes are the numbers from 1 to 6.
Let's write that down as a set $S$ : $S = \{1, 2, 3, 4, 5, 6\}$ There are $\bf{6}$ possible outcomes in total!

STEP 4

We're looking for the numbers less than 5.
From our set $S$ , these are 1, 2, 3, and 4.
Let's call this set of favorable outcomes $E$ : $E = \{1, 2, 3, 4\}$ So, there are $\bf{4}$ favorable outcomes.

STEP 5

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
In our case, the probability $P(E)$ is: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

STEP 6

We know there are $\bf{4}$ favorable outcomes (from the set $E$ ) and $\bf{6}$ total possible outcomes (from the set $S$ ).
Let's plug those numbers into our formula: $P(E) = \frac{4}{6}$

STEP 7

Now, let's simplify the fraction.
Both the numerator and denominator are divisible by 2.
Dividing both by 2 gives us: $P(E) = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}$

STEP 8

The probability of rolling a number less than 5 is $\frac{2}{3}$ .

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QuestionA standard die is rolled. Find the probability that the number rolled is less than 5. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer

Studdy Solution

STEP 1

What is this asking? What are the chances of rolling a number smaller than 5 on a regular six-sided die? Watch out! Don't include 5 itself; we only want numbers less than 5!

STEP 2

1. List the possible outcomes
2. List the favorable outcomes
3. Calculate the probability

STEP 3

When we roll a standard die, the possible outcomes are the numbers from 1 to 6.
Let's write that down as a set $S$ : $S = \{1, 2, 3, 4, 5, 6\}$ There are $\bf{6}$ possible outcomes in total!

STEP 4

We're looking for the numbers less than 5.
From our set $S$ , these are 1, 2, 3, and 4.
Let's call this set of favorable outcomes $E$ : $E = \{1, 2, 3, 4\}$ So, there are $\bf{4}$ favorable outcomes.

STEP 5

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
In our case, the probability $P(E)$ is: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

STEP 6

We know there are $\bf{4}$ favorable outcomes (from the set $E$ ) and $\bf{6}$ total possible outcomes (from the set $S$ ).
Let's plug those numbers into our formula: $P(E) = \frac{4}{6}$

STEP 7

Now, let's simplify the fraction.
Both the numerator and denominator are divisible by 2.
Dividing both by 2 gives us: $P(E) = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}$

STEP 8

The probability of rolling a number less than 5 is $\frac{2}{3}$ .

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QuestionA standard die is rolled. Find the probability that the number rolled is less than 5. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.Answer

Studdy Solution

STEP 1

What is this asking? What are the chances of rolling a number smaller than 5 on a regular six-sided die? Watch out! Don't include 5 itself; we only want numbers *less* than 5!

STEP 2

1. List the possible outcomes2. List the favorable outcomes3. Calculate the probability

STEP 3

When we roll a standard die, the possible outcomes are the numbers from 1 to 6.Let's write that down as a set SSS: S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}S={1,2,3,4,5,6} There are 6\bf{6}6 possible outcomes in total!

STEP 4

We're looking for the numbers *less* than 5.From our set SSS, these are 1, 2, 3, and 4.Let's call this set of favorable outcomes EEE: E={1,2,3,4}E = \{1, 2, 3, 4\}E={1,2,3,4} So, there are 4\bf{4}4 favorable outcomes.

STEP 5

STEP 6

We know there are 4\bf{4}4 favorable outcomes (from the set EEE) and 6\bf{6}6 total possible outcomes (from the set SSS).Let's plug those numbers into our formula: P(E)=46P(E) = \frac{4}{6}P(E)=64​

STEP 7

Now, let's simplify the fraction.Both the numerator and denominator are divisible by 2.Dividing both by 2 gives us: P(E)=4÷26÷2=23P(E) = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}P(E)=6÷24÷2​=32​

STEP 8

The probability of rolling a number less than 5 is 23\frac{2}{3}32​.

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QuestionA standard die is rolled. Find the probability that the number rolled is less than 5. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer

What is this asking? What are the chances of rolling a number smaller than 5 on a regular six-sided die? Watch out! Don't include 5 itself; we only want numbers less than 5!

1. List the possible outcomes
2. List the favorable outcomes
3. Calculate the probability

When we roll a standard die, the possible outcomes are the numbers from 1 to 6.
Let's write that down as a set $S$ : $S = \{1, 2, 3, 4, 5, 6\}$ There are $\bf{6}$ possible outcomes in total!

We're looking for the numbers less than 5.
From our set $S$ , these are 1, 2, 3, and 4.
Let's call this set of favorable outcomes $E$ : $E = \{1, 2, 3, 4\}$ So, there are $\bf{4}$ favorable outcomes.

We know there are $\bf{4}$ favorable outcomes (from the set $E$ ) and $\bf{6}$ total possible outcomes (from the set $S$ ).
Let's plug those numbers into our formula: $P(E) = \frac{4}{6}$

Now, let's simplify the fraction.
Both the numerator and denominator are divisible by 2.
Dividing both by 2 gives us: $P(E) = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}$

The probability of rolling a number less than 5 is $\frac{2}{3}$ .