Question

BRAINLIEST + Points please help me

John and Ted have a reputation for being late to events. If John is late 20% of the time, and Ted is late 40% of the time, what is the probability that both John and Ted will be on time? Show your work or explain how you got your answer.

Answer 1

Hello!

The answer is:

The probability that both John and Ted will be on time is 48%.

Why?

Since we are dealing with percentages, in order to make it easy to understand, let's remember that percentages are used to simplify the way we refer to something, talking in numeric terms. For example, meaning 100% it's equal to say that somethinh is complete, or absolute. Also, we can see the percentage as a ratio that is expressed as a fraction of the number 100 or $\frac{1}{100}$

From the statement the know that John is late 20% of the time, making it easy to understand, it's equal to say that from 100 times, John is late 20 times.

So, calculating we have:

For John:

$Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-20=80$

So, we have that the probability that John will be on time is 80%.

For Ted:

$Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-40=60$

So, we have that the probability that Ted will be on time is 60%.

Now, to calculate the probability that both John and Ted will be on time, we need to calculate the combined probability. It can be calculated using the following equation:

$CombinedProbability=Probability_{1}*Probability_{2}$

Let be:

$Probability_{1}=80(percent)=\frac{80}{100}=0.8\\\\Probability_{2}=60(percent)=\frac{60}{100}=0.6$

So, substituting and calculating we have:

$CombinedProbability=Probability_{1}*Probability_{2}$

$CombinedProbability=0.8*0.6=0.48=48(percent)$

Hence, we have that the probability that both John and Ted will be on time is 48%.

Have a nice day!