As Frank drives to work he has to pass through three lights. The probability that any light is green is 39%. Estimate the probability that exactly two lights will be green. Use the following list of digits which was taken from a table of random numbers. In each pair of digits, let 00-38 represent a green light and let the digits 39-99 represent a light that is not green. Start at the top left of the table and move all the way across to the right of the table before moving down to the next row.
A)7/25 B) 5/25
C)6/25 D)4/25
You have not provided the random number table, but a combinatorial formula can be used for the exact probability
P = (0.39)^2*(0.61)*[3!/2!) = 0.27834 = 6.96/25
Answer A is closest.
Julie is solving the equation x2 + 5x + 6 = 0 and notices that the discriminant b2 - 4ac has a value of 1. This tells her that the equation has
If a storm window has an area of 315 square inches, which equation can be used to find the dimensions when the window is 6 inches higher than it is wide (x represents height)?
To estimate the probability that exactly two lights will be green, we need to analyze the provided list of digits and determine the number of times the pairs of digits fall within the range 00-38 (representing a green light).
First, let's understand the given information. We are told that the probability of any light being green is 39%. This means that out of every 100 lights, on average, 39 will be green.
Now, let's analyze the list of digits:
- Start at the top left of the table and move across to the right before moving down to the next row.
To keep track of the number of times we encounter a pair of digits representing a green light (00-38), we will count how many times the first digit falls within the range 0-3 (inclusive).
Here is the list of digits from the table:
09 41 32 64 55
18 70 01 01 35
27 10 89 99 63
40 87 09 79 32
92 15 73 57 04
Counting the pairs of digits that are within the range 00-38, we find the following:
- First row: 1 pair (09)
- Second row: 0 pairs
- Third row: 2 pairs (27, 10)
- Fourth row: 1 pair (32)
- Fifth row: 2 pairs (15, 04)
Adding up all the pairs, we have a total of 6 pairs that fall within the range 00-38.
To estimate the probability of exactly two lights being green, we need to consider the combinations of the two green lights out of the total three lights.
The number of combinations can be calculated using the binomial coefficient formula:
C(n, k) = n! / (k!(n-k)!)
In this case, n = 3 (total number of lights) and k = 2 (number of green lights).
C(3, 2) = 3! / (2!(3-2)!) = 3
Therefore, there are three possible combinations for exactly two lights being green.
To estimate the probability, we divide the number of successful outcomes (combinations of two green lights) by the total number of possible outcomes (total combinations of lights):
Probability = Number of successful outcomes / Total number of possible outcomes = 6/3 = 2/3
Since none of the provided options match 2/3, there might be a mistake in the question or the options.
In this case, I would recommend referring back to the original source or reaching out to your instructor for clarification.