QuestionEvents $A$ and $B$ are independent. If $P(A) = 0.88$ and $P(A \text{ and } B) = 0.2$ , find $P(B)$ rounded to three decimals.

Studdy Solution

STEP 1

Assumptions1. Events $A$ and $B$ are independent. . The probability of event $A$ , $(A)$ , is0.88.
3. The probability of both events $A$ and $B$ occurring, $(A \text{ and } B)$ , is0..

STEP 2

For independent events, the probability of both events occurring is the product of their individual probabilities. This can be expressed as $(A \text{ and } B) =(A) \times(B)$

STEP 3

We can rearrange the equation from2 to solve for $(B)$ $(B) = \frac{(A \text{ and } B)}{(A)}$

STEP 4

Now, plug in the given values for $(A)$ and $(A \text{ and } B)$ to calculate $(B)$ $(B) = \frac{0.2}{0.88}$

STEP 5

Calculate the value of $(B)$ $(B) = \frac{0.2}{0.88} =0.22727$

STEP 6

The problem asks for the answer to be rounded to three decimal places. So, we round $(B)$ to three decimal places $(B) =0.227$ The probability of event $B$ , $(B)$ , is0.227.

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QuestionEvents $A$ and $B$ are independent. If $P(A) = 0.88$ and $P(A \text{ and } B) = 0.2$ , find $P(B)$ rounded to three decimals.

Studdy Solution

STEP 1

Assumptions1. Events $A$ and $B$ are independent. . The probability of event $A$ , $(A)$ , is0.88.
3. The probability of both events $A$ and $B$ occurring, $(A \text{ and } B)$ , is0..

STEP 2

For independent events, the probability of both events occurring is the product of their individual probabilities. This can be expressed as $(A \text{ and } B) =(A) \times(B)$

STEP 3

We can rearrange the equation from2 to solve for $(B)$ $(B) = \frac{(A \text{ and } B)}{(A)}$

STEP 4

Now, plug in the given values for $(A)$ and $(A \text{ and } B)$ to calculate $(B)$ $(B) = \frac{0.2}{0.88}$

STEP 5

Calculate the value of $(B)$ $(B) = \frac{0.2}{0.88} =0.22727$

STEP 6

The problem asks for the answer to be rounded to three decimal places. So, we round $(B)$ to three decimal places $(B) =0.227$ The probability of event $B$ , $(B)$ , is0.227.

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QuestionEvents AAA and BBB are independent. If P(A)=0.88P(A) = 0.88P(A)=0.88 and P(A and B)=0.2P(A \text{ and } B) = 0.2P(A and B)=0.2, find P(B)P(B)P(B) rounded to three decimals.

Studdy Solution

STEP 1

Assumptions1. Events AAA and BBB are independent. . The probability of event AAA, (A)(A)(A), is0.88.3. The probability of both events AAA and BBB occurring, (A and B)(A \text{ and } B)(A and B), is0..

STEP 2

For independent events, the probability of both events occurring is the product of their individual probabilities. This can be expressed as(A and B)=(A)×(B)(A \text{ and } B) =(A) \times(B)(A and B)=(A)×(B)

STEP 3

We can rearrange the equation from2 to solve for (B)(B)(B)(B)=(A and B)(A)(B) = \frac{(A \text{ and } B)}{(A)}(B)=(A)(A and B)​

STEP 4

Now, plug in the given values for (A)(A)(A) and (A and B)(A \text{ and } B)(A and B) to calculate (B)(B)(B)(B)=0.20.88(B) = \frac{0.2}{0.88}(B)=0.880.2​

STEP 5

Calculate the value of (B)(B)(B)(B)=0.20.88=0.22727(B) = \frac{0.2}{0.88} =0.22727(B)=0.880.2​=0.22727

STEP 6

The problem asks for the answer to be rounded to three decimal places. So, we round (B)(B)(B) to three decimal places(B)=0.227(B) =0.227(B)=0.227The probability of event BBB, (B)(B)(B), is0.227.

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QuestionEvents $A$ and $B$ are independent. If $P(A) = 0.88$ and $P(A \text{ and } B) = 0.2$ , find $P(B)$ rounded to three decimals.

Assumptions1. Events $A$ and $B$ are independent. . The probability of event $A$ , $(A)$ , is0.88.
3. The probability of both events $A$ and $B$ occurring, $(A \text{ and } B)$ , is0..

For independent events, the probability of both events occurring is the product of their individual probabilities. This can be expressed as $(A \text{ and } B) =(A) \times(B)$

We can rearrange the equation from2 to solve for $(B)$ $(B) = \frac{(A \text{ and } B)}{(A)}$

Now, plug in the given values for $(A)$ and $(A \text{ and } B)$ to calculate $(B)$ $(B) = \frac{0.2}{0.88}$

Calculate the value of $(B)$ $(B) = \frac{0.2}{0.88} =0.22727$

The problem asks for the answer to be rounded to three decimal places. So, we round $(B)$ to three decimal places $(B) =0.227$ The probability of event $B$ , $(B)$ , is0.227.