Probability of Getting Different Length Nails
a) What is the probability of reaching into the bin and getting a 4-inch nail?
A. Probability of getting a 4-inch nail: 451 / 1,419 ≈ 0.317 or 31.7%
b) What is the probability of getting a 5-inch nail?
B. Probability of getting a 5-inch nail: 33 / 1,419 ≈ 0.023 or 2.3%
c) If a particular application requires a nail that is 3 inches or shorter, what is the probability of getting a nail that will satisfy the requirements of the application?
And the application (3 inches or shorter) is approximately 0.658 or 65.8%
a) What is the probability of reaching into the bin and getting a 4-inch nail?
To calculate the probability of reaching into the bin and getting a 4-inch nail, we need to determine the total number of nails in the bin and the number of 4-inch nails in the bin. Total number of nails in the bin: 651 (1-inch) + 243 (2-inch) + 41 (3-inch) + 451 (4-inch) + 33 (5-inch) = 1,419. Number of 4-inch nails in the bin: 451. Probability of getting a 4-inch nail = Number of 4-inch nails / Total number of nails = 451 / 1,419 ≈ 0.317 or 31.7%
b) What is the probability of getting a 5-inch nail?
Similarly, to calculate the probability of getting a 5-inch nail, we divide the number of 5-inch nails in the bin by the total number of nails in the bin. Number of 5-inch nails in the bin: 33. Probability of getting a 5-inch nail = Number of 5-inch nails / Total number of nails = 33 / 1,419 ≈ 0.023 or 2.3%
c) If a particular application requires a nail that is 3 inches or shorter, what is the probability of getting a nail that will satisfy the requirements of the application?
If the requirement is for a nail that is 3 inches or shorter, we need to calculate the probability of getting a nail of 3 inches or shorter. This can be done by summing up the number of nails that satisfy the requirement (1-inch, 2-inch, and 3-inch) and dividing it by the total number of nails in the bin. Number of nails of 3 inches or shorter in the bin: 651 (1-inch) + 243 (2-inch) + 41 (3-inch) = 935. Probability of getting a nail of 3 inches or shorter = Number of nails of 3 inches or shorter / Total number of nails = 935 / 1,419 ≈ 0.658 or 65.8%. So, the probability of getting a nail that satisfies the requirements of the application (3 inches or shorter) is approximately 0.658 or 65.8%.