A teacher asks each student in the class to randomly choose a number between 1 to 80 and write it down. Devon and Michiko write down a number. What is the probability that both of their choices will be greater than 60? Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
0.25
0.06
0.938
0.063
80 - 60 = 20
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
20/60 * 20/60 = ?
To find the probability that both Devon and Michiko choose a number greater than 60, we first need to determine the total number of possible choices for both students.
Since each student can choose any number between 1 to 80, the total number of possible choices for each student is 80.
Now, we need to determine the number of choices that satisfy the condition of being greater than 60 for both students.
The number of choices greater than 60 for Devon is 80 - 60 = 20.
Similarly, the number of choices greater than 60 for Michiko is also 20.
To find the total number of choices that satisfy the condition for both students, we multiply the number of choices for each student since the choices are independent.
Total number of choices = 20 * 20 = 400
Since each student has 80 choices, the total number of possible choices is 80 * 80 = 6400.
Finally, we can determine the probability by dividing the total number of choices that satisfy the condition by the total number of possible choices.
Probability = 400 / 6400 = 0.0625
Rounded to the nearest thousandth, the probability is approximately 0.063.
Therefore, the answer is 0.063.
To find the probability that both Devon and Michiko's choices will be greater than 60, we first need to determine the total number of possible choices for each student, as well as the number of choices that satisfy the given condition.
There are a total of 80 numbers to choose from for each student (1 to 80).
Out of these 80 numbers, there are 20 numbers greater than 60 (61 to 80).
The probability of Devon choosing a number greater than 60 is 20/80 = 1/4 = 0.25.
Once Devon has made his choice, there are now 79 numbers left for Michiko to choose from, and 19 numbers greater than 60 (excluding the number chosen by Devon).
Therefore, the probability of Michiko choosing a number greater than 60, given that Devon already chose a number greater than 60, is 19/79.
To find the probability that both Devon and Michiko choose numbers greater than 60, we multiply their individual probabilities:
Probability = Probability of Devon's choice * Probability of Michiko's choice given Devon's choice
= 0.25 * (19/79)
= 0.063
Therefore, the probability that both of their choices will be greater than 60 is 0.063 (rounded to the nearest thousandth).