Math / Data & Statistics

QuestionYou pick a card at random. Without putting the first card back, you pick a second card at random.
3 45
What is the probability of picking a 5 and then picking a 3 ? Simplify your answer and write it as a fraction or whole number. $\square$

Studdy Solution

STEP 1

What is this asking? What are the chances of grabbing a 5 and then a 3 from a set of cards numbered 3, 4, and 5, if we don't put the first card back? Watch out! Don't forget that taking the first card changes what's left for the second pick!

STEP 2

1. Probability of picking a 5 first
2. Probability of picking a 3 second
3. Combined probability

STEP 3

Alright, let's start with the first pick!
We've got three cards: 3, 4, and 5.
We want to grab a 5.

STEP 4

There's only one 5, and three cards total.
So, the probability of picking a 5 first is $\frac{1}{3}$ .
Easy peasy!

STEP 5

Now, here's where it gets interesting.
We've already taken out a card (the 5).
So, we only have two cards left: 3 and 4.

STEP 6

We want a 3.
There's only one 3, and two cards total.
So, the probability of picking a 3 after picking a 5 is $\frac{1}{2}$ .

STEP 7

To get the probability of both events happening, we multiply the individual probabilities together.
Think of it like this: the chance of the first thing happening and the second thing happening depends on both probabilities!

STEP 8

So, we multiply the probability of picking a 5 first ( $\frac{1}{3}$ ) by the probability of picking a 3 second ( $\frac{1}{2}$ ):
$\frac{1}{3} \cdot \frac{1}{2} = \frac{1 \cdot 1}{3 \cdot 2} = \frac{1}{6}$

STEP 9

The probability of picking a 5 and then a 3 is $\frac{1}{6}$ !

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QuestionYou pick a card at random. Without putting the first card back, you pick a second card at random.
3 45
What is the probability of picking a 5 and then picking a 3 ? Simplify your answer and write it as a fraction or whole number. $\square$

Studdy Solution

STEP 1

What is this asking? What are the chances of grabbing a 5 and then a 3 from a set of cards numbered 3, 4, and 5, if we don't put the first card back? Watch out! Don't forget that taking the first card changes what's left for the second pick!

STEP 2

1. Probability of picking a 5 first
2. Probability of picking a 3 second
3. Combined probability

STEP 3

Alright, let's start with the first pick!
We've got three cards: 3, 4, and 5.
We want to grab a 5.

STEP 4

There's only one 5, and three cards total.
So, the probability of picking a 5 first is $\frac{1}{3}$ .
Easy peasy!

STEP 5

Now, here's where it gets interesting.
We've already taken out a card (the 5).
So, we only have two cards left: 3 and 4.

STEP 6

We want a 3.
There's only one 3, and two cards total.
So, the probability of picking a 3 after picking a 5 is $\frac{1}{2}$ .

STEP 7

To get the probability of both events happening, we multiply the individual probabilities together.
Think of it like this: the chance of the first thing happening and the second thing happening depends on both probabilities!

STEP 8

So, we multiply the probability of picking a 5 first ( $\frac{1}{3}$ ) by the probability of picking a 3 second ( $\frac{1}{2}$ ):
$\frac{1}{3} \cdot \frac{1}{2} = \frac{1 \cdot 1}{3 \cdot 2} = \frac{1}{6}$

STEP 9

The probability of picking a 5 and then a 3 is $\frac{1}{6}$ !

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QuestionYou pick a card at random. Without putting the first card back, you pick a second card at random.3 45What is the probability of picking a 5 and then picking a 3 ? Simplify your answer and write it as a fraction or whole number. □\square□

Studdy Solution

STEP 1

What is this asking? What are the chances of grabbing a 5 and *then* a 3 from a set of cards numbered 3, 4, and 5, if we *don't* put the first card back? Watch out! Don't forget that taking the first card *changes* what's left for the second pick!

STEP 2

1. Probability of picking a 5 first2. Probability of picking a 3 second3. Combined probability

STEP 3

Alright, let's **start** with the first pick!We've got three cards: 3, 4, and 5.We want to grab a 5.

STEP 4

There's only **one** 5, and **three** cards total.So, the probability of picking a 5 first is 13\frac{1}{3}31​.Easy peasy!

STEP 5

Now, here's where it gets interesting.We've *already* taken out a card (the 5).So, we only have **two** cards left: 3 and 4.

STEP 6

We want a 3.There's only **one** 3, and **two** cards total.So, the probability of picking a 3 *after* picking a 5 is 12\frac{1}{2}21​.

STEP 7

To get the probability of *both* events happening, we **multiply** the individual probabilities together.Think of it like this: the chance of the first thing happening *and* the second thing happening depends on both probabilities!

STEP 8

So, we multiply the probability of picking a 5 first (13\frac{1}{3}31​) by the probability of picking a 3 second (12\frac{1}{2}21​):13⋅12=1⋅13⋅2=16 \frac{1}{3} \cdot \frac{1}{2} = \frac{1 \cdot 1}{3 \cdot 2} = \frac{1}{6} 31​⋅21​=3⋅21⋅1​=61​

STEP 9

The probability of picking a 5 and then a 3 is 16\frac{1}{6}61​!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionYou pick a card at random. Without putting the first card back, you pick a second card at random.
3 45
What is the probability of picking a 5 and then picking a 3 ? Simplify your answer and write it as a fraction or whole number. $\square$

What is this asking? What are the chances of grabbing a 5 and then a 3 from a set of cards numbered 3, 4, and 5, if we don't put the first card back? Watch out! Don't forget that taking the first card changes what's left for the second pick!

1. Probability of picking a 5 first
2. Probability of picking a 3 second
3. Combined probability

Alright, let's start with the first pick!
We've got three cards: 3, 4, and 5.
We want to grab a 5.

There's only one 5, and three cards total.
So, the probability of picking a 5 first is $\frac{1}{3}$ .
Easy peasy!

Now, here's where it gets interesting.
We've already taken out a card (the 5).
So, we only have two cards left: 3 and 4.

We want a 3.
There's only one 3, and two cards total.
So, the probability of picking a 3 after picking a 5 is $\frac{1}{2}$ .

To get the probability of both events happening, we multiply the individual probabilities together.
Think of it like this: the chance of the first thing happening and the second thing happening depends on both probabilities!

So, we multiply the probability of picking a 5 first ( $\frac{1}{3}$ ) by the probability of picking a 3 second ( $\frac{1}{2}$ ):
$\frac{1}{3} \cdot \frac{1}{2} = \frac{1 \cdot 1}{3 \cdot 2} = \frac{1}{6}$

The probability of picking a 5 and then a 3 is $\frac{1}{6}$ !