Math / Data & Statistics

QuestionYou flip a coin twice.
What is the probability of getting tails and then getting tails? 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 flipping a coin twice and getting tails both times? Watch out! Don't mix up "and" and "or" probability! "And" means both events must happen.

STEP 2

1. Probability of first flip
2. Probability of second flip
3. Combined probability

STEP 3

Alright, let's start with the first flip!
What's the probability of getting tails?
Well, a coin has two sides: heads and tails.
Assuming it's a fair coin, there's only one way to get tails out of two possible outcomes.

STEP 4

So, the probability of getting tails on the first flip is $\frac{1}{2}$ .
One favorable outcome (tails) divided by two total outcomes (heads or tails).

STEP 5

Now for the second flip!
It's the same situation as the first flip.
We still have one way to get tails out of two possible outcomes.

STEP 6

So, the probability of getting tails on the second flip is also $\frac{1}{2}$ .

STEP 7

Here's the exciting part!
We want both flips to be tails.
When we want two events to happen in a row, we multiply their probabilities.
Why? Because the second flip's outcome is independent of the first flip's outcome!

STEP 8

So, the probability of getting tails and then tails is: $\frac{1}{2} \cdot \frac{1}{2}$

STEP 9

Let's calculate that: $\frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4}$

STEP 10

The probability of getting tails and then tails is $\frac{1}{4}$ .

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QuestionYou flip a coin twice.
What is the probability of getting tails and then getting tails? 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 flipping a coin twice and getting tails both times? Watch out! Don't mix up "and" and "or" probability! "And" means both events must happen.

STEP 2

1. Probability of first flip
2. Probability of second flip
3. Combined probability

STEP 3

Alright, let's start with the first flip!
What's the probability of getting tails?
Well, a coin has two sides: heads and tails.
Assuming it's a fair coin, there's only one way to get tails out of two possible outcomes.

STEP 4

So, the probability of getting tails on the first flip is $\frac{1}{2}$ .
One favorable outcome (tails) divided by two total outcomes (heads or tails).

STEP 5

Now for the second flip!
It's the same situation as the first flip.
We still have one way to get tails out of two possible outcomes.

STEP 6

So, the probability of getting tails on the second flip is also $\frac{1}{2}$ .

STEP 7

Here's the exciting part!
We want both flips to be tails.
When we want two events to happen in a row, we multiply their probabilities.
Why? Because the second flip's outcome is independent of the first flip's outcome!

STEP 8

So, the probability of getting tails and then tails is: $\frac{1}{2} \cdot \frac{1}{2}$

STEP 9

Let's calculate that: $\frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4}$

STEP 10

The probability of getting tails and then tails is $\frac{1}{4}$ .

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QuestionYou flip a coin twice.What is the probability of getting tails and then getting tails? 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 flipping a coin twice and getting tails both times? Watch out! Don't mix up "and" and "or" probability! "And" means *both* events must happen.

STEP 2

1. Probability of first flip2. Probability of second flip3. Combined probability

STEP 3

Alright, let's **start** with the first flip!What's the probability of getting tails?Well, a coin has two sides: heads and tails.Assuming it's a fair coin, there's only **one** way to get tails out of **two** possible outcomes.

STEP 4

So, the probability of getting tails on the first flip is 12\frac{1}{2}21​.One **favorable outcome** (tails) divided by **two total outcomes** (heads or tails).

STEP 5

Now for the second flip!It's the same situation as the first flip.We still have **one** way to get tails out of **two** possible outcomes.

STEP 6

So, the probability of getting tails on the second flip is *also* 12\frac{1}{2}21​.

STEP 7

Here's the exciting part!We want *both* flips to be tails.When we want two events to happen in a row, we **multiply** their probabilities.Why? Because the second flip's outcome is independent of the first flip's outcome!

STEP 8

So, the probability of getting tails and *then* tails is: 12⋅12 \frac{1}{2} \cdot \frac{1}{2} 21​⋅21​

STEP 9

Let's **calculate** that: 12⋅12=1⋅12⋅2=14 \frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4} 21​⋅21​=2⋅21⋅1​=41​

STEP 10

The probability of getting tails and then tails is 14\frac{1}{4}41​.

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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 flip a coin twice.
What is the probability of getting tails and then getting tails? Simplify your answer and write it as a fraction or whole number. $\square$

What is this asking? What are the chances of flipping a coin twice and getting tails both times? Watch out! Don't mix up "and" and "or" probability! "And" means both events must happen.

1. Probability of first flip
2. Probability of second flip
3. Combined probability

Alright, let's start with the first flip!
What's the probability of getting tails?
Well, a coin has two sides: heads and tails.
Assuming it's a fair coin, there's only one way to get tails out of two possible outcomes.

So, the probability of getting tails on the first flip is $\frac{1}{2}$ .
One favorable outcome (tails) divided by two total outcomes (heads or tails).

Now for the second flip!
It's the same situation as the first flip.
We still have one way to get tails out of two possible outcomes.

So, the probability of getting tails on the second flip is also $\frac{1}{2}$ .

Here's the exciting part!
We want both flips to be tails.
When we want two events to happen in a row, we multiply their probabilities.
Why? Because the second flip's outcome is independent of the first flip's outcome!

So, the probability of getting tails and then tails is: $\frac{1}{2} \cdot \frac{1}{2}$

Let's calculate that: $\frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4}$

The probability of getting tails and then tails is $\frac{1}{4}$ .