Math / Data & Statistics

QuestionUntitled document -... Traditional | Stats | N... Defense | Stats | NBA... Utah vs LA Stats \& P... Ivica Zubac /// Stats /... Home - Northern Ess... Content Midterm Exam: Ch $1(1,2) \mathbf{2}(1,2,3) 3(1,2,3) 4(1,2) 5(1,2,3) 6(1,2)$ Time Remaining: 58:14 Jona Question 26 of 30 (1 point) | Question Attempt: 1 of 1 < 13 $\equiv 14$ $\equiv 15$ 16 $=18$ $=19$ $=20$ $=21$ $=22$ $\equiv 23$
A fair coin is tossed four times. What is the probability that the sequence of tosses is HHHH? Write your answer as a fraction or a decimal, rounded to four decimal places.
The probability that the sequence of tosses is HHHH is $\square$ .

Studdy Solution

STEP 1

What is this asking? What are the chances of flipping a normal coin four times and getting heads every single time? Watch out! Don't forget that each coin flip is independent of the others!

STEP 2

1. Calculate the probability of a single heads.
2. Calculate the probability of four heads in a row.

STEP 3

Alright, so we've got a fair coin.
That's math-speak for a coin that has an equal chance of landing on heads or tails.

STEP 4

Since there are only two possible outcomes (heads or tails), the probability of getting heads on a single flip is one out of two, or $\frac{1}{2}$ .
It's like choosing the winning door on a game show, but with only two doors and one amazing prize behind the "heads" door!

STEP 5

Now, we want to know the probability of getting heads four times in a row.
Since each flip is independent, we can just multiply the probabilities of getting heads on each individual flip.
It's like winning that game show four times in a row!

STEP 6

So, the probability of HHHH is: $\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}$

STEP 7

Let's multiply those fractions.
Remember, when multiplying fractions, we multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together: $\frac{1 \cdot 1 \cdot 1 \cdot 1}{2 \cdot 2 \cdot 2 \cdot 2} = \frac{1}{16}$

STEP 8

The problem asks for the answer as a fraction or a decimal rounded to four decimal places.
Let's convert our fraction to a decimal by dividing the numerator ( $1$ ) by the denominator ( $16$ ): $\frac{1}{16} = 0.0625$

STEP 9

The probability of getting four heads in a row is $\frac{1}{16}$ or $0.0625$ .

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Studdy Solution

STEP 1

What is this asking? What are the chances of flipping a normal coin four times and getting heads every single time? Watch out! Don't forget that each coin flip is independent of the others!

STEP 2

1. Calculate the probability of a single heads.
2. Calculate the probability of four heads in a row.

STEP 3

Alright, so we've got a fair coin.
That's math-speak for a coin that has an equal chance of landing on heads or tails.

STEP 4

Since there are only two possible outcomes (heads or tails), the probability of getting heads on a single flip is one out of two, or $\frac{1}{2}$ .
It's like choosing the winning door on a game show, but with only two doors and one amazing prize behind the "heads" door!

STEP 5

Now, we want to know the probability of getting heads four times in a row.
Since each flip is independent, we can just multiply the probabilities of getting heads on each individual flip.
It's like winning that game show four times in a row!

STEP 6

So, the probability of HHHH is: $\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}$

STEP 7

Let's multiply those fractions.
Remember, when multiplying fractions, we multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together: $\frac{1 \cdot 1 \cdot 1 \cdot 1}{2 \cdot 2 \cdot 2 \cdot 2} = \frac{1}{16}$

STEP 8

The problem asks for the answer as a fraction or a decimal rounded to four decimal places.
Let's convert our fraction to a decimal by dividing the numerator ( $1$ ) by the denominator ( $16$ ): $\frac{1}{16} = 0.0625$

STEP 9

The probability of getting four heads in a row is $\frac{1}{16}$ or $0.0625$ .

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Studdy Solution

STEP 1

What is this asking? What are the chances of flipping a normal coin four times and getting heads every single time? Watch out! Don't forget that each coin flip is independent of the others!

STEP 2

1. Calculate the probability of a single heads.2. Calculate the probability of four heads in a row.

STEP 3

Alright, so we've got a *fair* coin.That's math-speak for a coin that has an equal chance of landing on heads or tails.

STEP 4

Since there are only two possible outcomes (heads or tails), the probability of getting heads on a single flip is one out of two, or 12\frac{1}{2}21​.It's like choosing the winning door on a game show, but with only two doors and one amazing prize behind the "heads" door!

STEP 5

Now, we want to know the probability of getting heads *four times in a row*.Since each flip is independent, we can just multiply the probabilities of getting heads on each individual flip.It's like winning that game show four times in a row!

STEP 6

So, the probability of HHHH is: 12⋅12⋅12⋅12 \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} 21​⋅21​⋅21​⋅21​

STEP 7

STEP 8

The problem asks for the answer as a fraction or a decimal rounded to four decimal places.Let's convert our fraction to a decimal by dividing the numerator (111) by the denominator (161616): 116=0.0625 \frac{1}{16} = 0.0625 161​=0.0625

STEP 9

The probability of getting four heads in a row is 116\frac{1}{16}161​ or 0.06250.06250.0625.

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1. Calculate the probability of a single heads.
2. Calculate the probability of four heads in a row.

Alright, so we've got a fair coin.
That's math-speak for a coin that has an equal chance of landing on heads or tails.

Since there are only two possible outcomes (heads or tails), the probability of getting heads on a single flip is one out of two, or $\frac{1}{2}$ .
It's like choosing the winning door on a game show, but with only two doors and one amazing prize behind the "heads" door!

Now, we want to know the probability of getting heads four times in a row.
Since each flip is independent, we can just multiply the probabilities of getting heads on each individual flip.
It's like winning that game show four times in a row!

So, the probability of HHHH is: $\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}$

The problem asks for the answer as a fraction or a decimal rounded to four decimal places.
Let's convert our fraction to a decimal by dividing the numerator ( $1$ ) by the denominator ( $16$ ): $\frac{1}{16} = 0.0625$

The probability of getting four heads in a row is $\frac{1}{16}$ or $0.0625$ .