A stick of 70 cm breaks in two. At both ends (each 10cm) the stick cannot break. All places where the stick can break are equally likely. What is the probability that the difference between the largest and the smallest part of the stick is at least 10cm?
If the break is x cm from one end, then you want
|x - (70-x)| >= 10
So, either
x <= 30 OR x >= 40
That means there is only an interval of 10cm which will not work.
So, since the total breakable interval is 50cm, there is a 40/50 chance of breaking at an acceptable spot.
thank you
To find the probability that the difference between the largest and the smallest part of the stick is at least 10cm, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's consider the possible lengths of the largest part of the stick. Since each end (10cm) cannot be broken, the largest part can range from 10cm to 50cm.
Now, let's consider the length of the smallest part of the stick. Since the difference between the largest and smallest part must be at least 10cm, the smallest part must have a length from 0cm to 30cm.
To find the total number of possible outcomes, we need to calculate the area of the rectangle formed by the possible lengths of the largest and smallest parts.
Rectangle area = length of largest part * length of smallest part
= (50 - 10) cm * (30 - 0) cm
= 40 cm * 30 cm
= 1200 cm^2
To find the number of favorable outcomes, we need to calculate the area of the rectangle formed by the lengths of the largest and smallest parts that satisfy the condition (difference >= 10cm).
Rectangle area = (length of largest part - 10 cm) * (length of smallest part)
= (40 - 10) cm * (30 - 0) cm
= 30 cm * 30 cm
= 900 cm^2
Therefore, the number of favorable outcomes is 900 cm^2.
The probability can now be calculated as the favorable outcomes divided by the total outcomes:
Probability = favorable outcomes / total outcomes
= 900 cm^2 / 1200 cm^2
= 0.75
Hence, the probability that the difference between the largest and smallest part of the stick is at least 10cm is 0.75 or 75%.