QuestionThree coins are flipped. Count total outcomes, outcomes where the second coin is heads, and find $P(A)$ .

Studdy Solution

STEP 1

Assumptions1. The coins are fair, meaning each coin has an equal chance of landing on heads or tails. . Three coins are flipped at the same time.
3. Each coin has two possible outcomes heads (H) or tails ().
4. The possible outcomes for the three coins being flipped are $\{H H H,, H H, H, H H, H, H H, H\}$ .
5. Event $A$ is defined as the event that the second coin flipped shows a head.

STEP 2

First, we need to find the total number of outcomes in the sample space. This is simply the total number of possible outcomes when flipping three coins.
The sample space, denoted as $$, is the set of all possible outcomes. In this case, $ = \{H H H,, H H, H, H H, H, H H, H\}$.

STEP 3

Count the number of outcomes in the sample space.
There are8 outcomes in the sample space.

STEP 4

Next, we need to find the number of outcomes in event $A$ . Event $A$ is defined as the event that the second coin flipped shows a head.
The outcomes in event $A$ are $\{H H H, H H, H H, H H\}$ .

STEP 5

Count the number of outcomes in event $A$ .
There are4 outcomes in event $A$ .

STEP 6

Now, we can calculate the probability of event $A$ , denoted as $(A)$ . The probability of an event is defined as the number of outcomes in the event divided by the total number of outcomes in the sample space.
$(A) = \frac{Number\, of\, outcomes\, in\, event\, A}{Total\, number\, of\, outcomes\, in\, the\, sample\, space}$

STEP 7

Plug in the values for the number of outcomes in event $A$ and the total number of outcomes in the sample space to calculate $(A)$ .
$(A) = \frac{4}{}$

STEP 8

Calculate the probability of event $A$ .
$(A) = \frac{4}{8} =0.5$ So, the probability that the second coin flipped shows heads is0.5.

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QuestionThree coins are flipped. Count total outcomes, outcomes where the second coin is heads, and find $P(A)$ .

Studdy Solution

STEP 1

STEP 2

First, we need to find the total number of outcomes in the sample space. This is simply the total number of possible outcomes when flipping three coins.
The sample space, denoted as $$, is the set of all possible outcomes. In this case, $ = \{H H H,, H H, H, H H, H, H H, H\}$.

STEP 3

Count the number of outcomes in the sample space.
There are8 outcomes in the sample space.

STEP 4

Next, we need to find the number of outcomes in event $A$ . Event $A$ is defined as the event that the second coin flipped shows a head.
The outcomes in event $A$ are $\{H H H, H H, H H, H H\}$ .

STEP 5

Count the number of outcomes in event $A$ .
There are4 outcomes in event $A$ .

STEP 6

STEP 7

Plug in the values for the number of outcomes in event $A$ and the total number of outcomes in the sample space to calculate $(A)$ .
$(A) = \frac{4}{}$

STEP 8

Calculate the probability of event $A$ .
$(A) = \frac{4}{8} =0.5$ So, the probability that the second coin flipped shows heads is0.5.

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QuestionThree coins are flipped. Count total outcomes, outcomes where the second coin is heads, and find P(A)P(A)P(A).

Studdy Solution

STEP 1

STEP 2

First, we need to find the total number of outcomes in the sample space. This is simply the total number of possible outcomes when flipping three coins.The sample space, denoted as $$, is the set of all possible outcomes. In this case, $ = \{H H H,, H H, H, H H, H, H H, H\}$.

STEP 3

Count the number of outcomes in the sample space.There are8 outcomes in the sample space.

STEP 4

Next, we need to find the number of outcomes in event AAA. Event AAA is defined as the event that the second coin flipped shows a head.The outcomes in event AAA are {HHH,HH,HH,HH}\{H H H, H H, H H, H H\}{HHH,HH,HH,HH}.

STEP 5

Count the number of outcomes in event AAA.There are4 outcomes in event AAA.

STEP 6

STEP 7

Plug in the values for the number of outcomes in event AAA and the total number of outcomes in the sample space to calculate (A)(A)(A).(A)=4(A) = \frac{4}{}(A)=4​

STEP 8

Calculate the probability of event AAA.(A)=48=0.5(A) = \frac{4}{8} =0.5(A)=84​=0.5So, the probability that the second coin flipped shows heads is0.5.

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QuestionThree coins are flipped. Count total outcomes, outcomes where the second coin is heads, and find $P(A)$ .

First, we need to find the total number of outcomes in the sample space. This is simply the total number of possible outcomes when flipping three coins.
The sample space, denoted as $$, is the set of all possible outcomes. In this case, $ = \{H H H,, H H, H, H H, H, H H, H\}$.

Count the number of outcomes in the sample space.
There are8 outcomes in the sample space.

Next, we need to find the number of outcomes in event $A$ . Event $A$ is defined as the event that the second coin flipped shows a head.
The outcomes in event $A$ are $\{H H H, H H, H H, H H\}$ .

Count the number of outcomes in event $A$ .
There are4 outcomes in event $A$ .

Plug in the values for the number of outcomes in event $A$ and the total number of outcomes in the sample space to calculate $(A)$ .
$(A) = \frac{4}{}$

Calculate the probability of event $A$ .
$(A) = \frac{4}{8} =0.5$ So, the probability that the second coin flipped shows heads is0.5.