QuestionWhat is the probability the alarm sounds when a student enters the lab at 12:36, given it sounds for 5 seconds every 5 minutes? F. $\frac{1}{300}$ G. $\frac{1}{60}$ H. $\frac{1}{59}$ J. $\frac{5}{59}$ K. $\frac{1}{5}$

Studdy Solution

STEP 1

Assumptions1. The alarm sounds randomly for5 seconds during every5 minute interval. . The5 minute intervals start at noon every day.
3. The student enters the laboratory at1236 in the afternoon.
4. We need to find the probability that the alarm will be sounding at the exact moment the student enters.

STEP 2

First, we need to understand the total time in seconds for each5 minute interval. There are60 seconds in a minute, so a5 minute interval is equivalent to300 seconds.
$Total\, time =5\, minutes \\times60\, seconds/minute =300\, seconds$

STEP 3

The alarm sounds for5 seconds during each5 minute interval. This is the favorable outcome we are interested in.
$avorable\, outcome =5\, seconds$

STEP 4

The probability of an event is calculated as the ratio of the favorable outcomes to the total possible outcomes. In this case, the favorable outcome is the alarm sounding ( seconds), and the total possible outcomes are the total seconds in a minute interval (300 seconds).
$Probability = \frac{avorable\, outcome}{Total\, possible\, outcomes}$

STEP 5

Plug in the values for the favorable outcome and the total possible outcomes to calculate the probability.
$Probability = \frac{5\, seconds}{300\, seconds}$

STEP 6

Calculate the probability.
$Probability = \frac{5}{300} = \frac{1}{60}$ The probability that the alarm will be sounding at the time the student enters the laboratory is $\frac{1}{60}$ .

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QuestionWhat is the probability the alarm sounds when a student enters the lab at 12:36, given it sounds for 5 seconds every 5 minutes? F. $\frac{1}{300}$ G. $\frac{1}{60}$ H. $\frac{1}{59}$ J. $\frac{5}{59}$ K. $\frac{1}{5}$

Studdy Solution

STEP 1

STEP 2

First, we need to understand the total time in seconds for each5 minute interval. There are60 seconds in a minute, so a5 minute interval is equivalent to300 seconds.
$Total\, time =5\, minutes \\times60\, seconds/minute =300\, seconds$

STEP 3

The alarm sounds for5 seconds during each5 minute interval. This is the favorable outcome we are interested in.
$avorable\, outcome =5\, seconds$

STEP 4

STEP 5

Plug in the values for the favorable outcome and the total possible outcomes to calculate the probability.
$Probability = \frac{5\, seconds}{300\, seconds}$

STEP 6

Calculate the probability.
$Probability = \frac{5}{300} = \frac{1}{60}$ The probability that the alarm will be sounding at the time the student enters the laboratory is $\frac{1}{60}$ .

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QuestionWhat is the probability the alarm sounds when a student enters the lab at 12:36, given it sounds for 5 seconds every 5 minutes? F. 1300\frac{1}{300}3001​ G. 160\frac{1}{60}601​ H. 159\frac{1}{59}591​ J. 559\frac{5}{59}595​ K. 15\frac{1}{5}51​

Studdy Solution

STEP 1

Assumptions1. The alarm sounds randomly for5 seconds during every5 minute interval. . The5 minute intervals start at noon every day.3. The student enters the laboratory at1236 in the afternoon.4. We need to find the probability that the alarm will be sounding at the exact moment the student enters.

STEP 2

STEP 3

The alarm sounds for5 seconds during each5 minute interval. This is the favorable outcome we are interested in.avorable outcome=5 secondsavorable\, outcome =5\, secondsavorableoutcome=5seconds

STEP 4

STEP 5

Plug in the values for the favorable outcome and the total possible outcomes to calculate the probability.Probability=5 seconds300 secondsProbability = \frac{5\, seconds}{300\, seconds}Probability=300seconds5seconds​

STEP 6

Calculate the probability.Probability=5300=160Probability = \frac{5}{300} = \frac{1}{60}Probability=3005​=601​The probability that the alarm will be sounding at the time the student enters the laboratory is 160\frac{1}{60}601​.

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QuestionWhat is the probability the alarm sounds when a student enters the lab at 12:36, given it sounds for 5 seconds every 5 minutes? F. $\frac{1}{300}$ G. $\frac{1}{60}$ H. $\frac{1}{59}$ J. $\frac{5}{59}$ K. $\frac{1}{5}$

The alarm sounds for5 seconds during each5 minute interval. This is the favorable outcome we are interested in.
$avorable\, outcome =5\, seconds$

Plug in the values for the favorable outcome and the total possible outcomes to calculate the probability.
$Probability = \frac{5\, seconds}{300\, seconds}$

Calculate the probability.
$Probability = \frac{5}{300} = \frac{1}{60}$ The probability that the alarm will be sounding at the time the student enters the laboratory is $\frac{1}{60}$ .