a hat contains a number od cubes: 15 red, 10 white, 5 blue and 20 black,20 years gone and i am back again. one cube at random. what is the probability that it is:
a) a red cube?
b) not a red cube?
c) a cube that is white or black?
d) a cube that is neither white nor black?
e) what do you answers to part a and b add up to and why?
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will start for you.
a) 15/total cubes = ?
b) (total cubes-15)/total cubes = ?
Either-or probabilities are found by adding the individual probabilities.
a. 30% or 0.3
b. 70% or 0.7
To solve this problem, we need to first find the total number of cubes in the hat, and then determine the number of cubes that meet the given conditions. Let's break it down step-by-step:
Step 1: Calculate the total number of cubes in the hat
The hat contains 15 red cubes, 10 white cubes, 5 blue cubes, and 20 black cubes. Therefore, the total number of cubes in the hat is:
15 red + 10 white + 5 blue + 20 black = 50 cubes
Now that we know there are 50 cubes in total, we can proceed to address each part of the question:
a) Probability of selecting a red cube:
Since there are 15 red cubes out of 50 total cubes, the probability of selecting a red cube can be calculated as:
Number of red cubes / Total number of cubes = 15 / 50 = 3/10 or 0.3 (30%)
b) Probability of not selecting a red cube:
The probability of not selecting a red cube is the complement of selecting a red cube. Therefore, we subtract the probability of selecting a red cube from 1:
1 - Probability of selecting a red cube = 1 - 0.3 = 0.7 (70%)
c) Probability of selecting a white or black cube:
To find the probability of selecting a white or black cube, we need to determine the total number of white and black cubes. This can be calculated as:
Number of white cubes + Number of black cubes = 10 + 20 = 30 cubes
Therefore, the probability of selecting a white or black cube can be calculated as:
Number of white or black cubes / Total number of cubes = 30 / 50 = 3/5 or 0.6 (60%)
d) Probability of selecting a cube that is neither white nor black:
To find the probability of selecting a cube that is neither white nor black, we need to calculate the number of blue cubes. There are 5 blue cubes in the hat. Therefore, the probability can be calculated as:
Number of blue cubes / Total number of cubes = 5 / 50 = 1/10 or 0.1 (10%)
e) Sum of probabilities of selecting a red cube and not selecting a red cube:
The sum of the probabilities in Parts a and b should always add up to 1. Here's why:
Part a: Probability of selecting a red cube = 0.3 (30%)
Part b: Probability of not selecting a red cube = 0.7 (70%)
When we add these two probabilities, we get:
0.3 + 0.7 = 1
The sum is always 1 because the probability of either event happening (either selecting a red cube or not selecting a red cube) must be certain or 100%.
I hope this explanation helps you understand the process of calculating probabilities based on the given information! Let me know if you have any further questions.