Question

A door alarm works in 72 out of 100 cases and surveillance camera works in 68 out of 100 cases. what is the probability of effective screening techniques keeping in mind that these two methods can be used together

Answer 1

A door alarm works in 72 out of 100 cases.

surveillance camera works in 68 out of 100 cases.

The probability that method A is used = 72/100

The probability that method B is used = 68/100

Since both method are used we find the probability of A and B

Probability ( A and B) = $\frac{72}{100}$ * $\frac{68}{100}$

= $\frac{306}{625}$

Answer 2

The probability of the effective screeningtechnique when both methods are used together is$\boxed{{\mathbf{0}}{\mathbf{.4896}}}$.

Further explanation:

It is given that the door alarm works in $72$ out of $100$ cases.

Probability is the chance of any event that is likely to occur. It is the ratio of number of favorable events and the total number of possible outcomes.

Since the door alarm works in $72$ out of $100$cases, the probability of the door alarm that is likely to occur is calculated by taking the ratio of the favorable events $72$ and the total number of possible outcome $100$ as follows:

$\begin{aligned}P\left( {{\text{door alarm}}} \right)&= \frac{{72}}{{100}} \\&=0.72\\ \end{aligned}$

Therefore, the probability of the door alarm is ${\mathbf{0}}{\mathbf{.72}}$.

It is given that the surveillance camera works in $68$ out of $100$ cases.

Since the surveillance camera works in $68$ out of $100$cases, the probability of the surveillance camera that is likely to occur is calculated by taking the ratio of the favorable events $68$ and the total number of possible outcome $100$ as follows:

$\begin{aligned} P\left( {{\text{surveillance camera}}} \right)&=\frac{{68}}{{100}} \\&=0.68\\\end{aligned}$

Therefore, the probability of the surveillance camera is ${\mathbf{0}}{\mathbf{.68}}$.

Now, when both methods that is door alarm or surveillance camera is used together, the probability of both events occurring together can be calculated by using a formula$P\left( {A \cap B} \right) = P\left( A \right) \times P\left( B \right)$.

Here, Event A is door alarm and Event B is surveillance camera.

The probability of the door alarm is ${\mathbf{0}}{\mathbf{.72}}$ that is$P\left( A \right) = 0.72$.

The probability of the surveillance camera is ${\mathbf{0}}{\mathbf{.68}}$that is$P\left( B \right) = 0.68$.

Substitute $0.72$ for $P\left( A \right)$ and $0.68$ for $P\left( B \right)$in equation $P\left( {A \cap B} \right) = P\left( A \right) \times P\left( B \right)$ to obtain theprobability of the effective screeningtechnique when both methods are used together.

$\begin{aligned} P\left( {A \cap B} \right)&= 0.72 \times 0.68\\&=0.4896\\\end{aligned}$

Therefore, the probability is$\boxed{{\mathbf{0}}{\mathbf{.4896}}}$.

Thus, theprobability of the effective screeningtechnique when both methods are used together is$\boxed{{\mathbf{0}}{\mathbf{.4896}}}$.

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Probability

Keywords:expression, probability, screening technique, camera, , two methods,