A bag contains 6 red marbles, 3 white marbles, and 7 blue marbles. You pick a marble without looking. Find the probability of drawing a white marble.
There are a total of 16 marbles in the bag. The probability of drawing a white marble is the number of white marbles divided by the total number of marbles:
P(white marble) = 3/16
Therefore, the probability of drawing a white marble is 3/16.
A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number less than 3. Find the probability of not rolling a number less than 3.
There are six possible outcomes when rolling a standard number cube: 1, 2, 3, 4, 5, or 6.
To find the probability of rolling a number less than 3, we need to identify the outcomes that satisfy this condition. There are two outcomes - rolling a 1 or rolling a 2 - that are less than 3. Therefore, the probability of rolling a number less than 3 is:
P(rolling a number less than 3) = 2/6 = 1/3
To find the probability of not rolling a number less than 3, we need to identify the outcomes that do not satisfy this condition. There are four outcomes - rolling a 3, 4, 5, or 6 - that do not satisfy this condition. Therefore, the probability of not rolling a number less than 3 is:
P(not rolling a number less than 3) = 4/6 = 2/3
A number cube is rolled 360 times and the results are recorded as follows: 54 ones, 60 twos, 66 threes, 71 fours, 35 fives, and 74 sixes. What is the experimental probability of rolling a two or a three?
The total number of rolls is:
54 + 60 + 66 + 71 + 35 + 74 = 360
The number of rolls that resulted in a two or a three is:
60 + 66 = 126
Therefore, the experimental probability of rolling a two or a three is:
126/360 = 0.35 (rounded to two decimal places)
So the experimental probability of rolling a two or a three is 0.35 or 35%.
From a barrel of colored marbles, you randomly select 3 blue, 2 yellow, 7 red, 8 green, and 2 purple marbles. Find the experimental probability of randomly selecting either a green or a purple marble.
The total number of marbles is:
3 + 2 + 7 + 8 + 2 = 22
The number of green and purple marbles is:
8 + 2 = 10
Therefore, the experimental probability of randomly selecting either a green or a purple marble is:
10/22 = 5/11 (which is approximately 0.45 when rounded to two decimal places)
So the experimental probability of randomly selecting either a green or a purple marble is 5/11 or approximately 0.45.
A standard number cube is rolled 180 times. Predict how many times a 3 or a 5 will be the result.
The probability of rolling a 3 or a 5 on a standard number cube is 2/6 or 1/3. This means that out of 180 rolls, we can expect:
180 * 1/3 = 60
So we would predict that 3 or 5 would be rolled about 60 times out of 180 rolls.
A new movie opened the other day. So far, 500,000 people have seen it. The producers of the movie needed to know if the people liked it. A random sample of 8,000 people were asked as they were leaving the theater if they liked the movie. Of those interviewed, 4,200 enjoyed the movie. Predict the total number of people who have enjoyed the movie.
We can set up a proportion to find the predicted number of people who enjoyed the movie based on the sample:
number of people who enjoyed the movie / total sample size = number of people who enjoyed the movie overall / total number of people who have seen the movie
We know that the sample size is 8,000 and the number of people who enjoyed the movie in the sample is 4,200. We also know that the total number of people who have seen the movie is 500,000. Let's use x to represent the number of people who enjoyed the movie overall. Then the proportion becomes:
4,200 / 8,000 = x / 500,000
To solve for x, we can cross-multiply and simplify:
4,200 * 500,000 = 8,000 * x
2,100,000,000 = 8,000x
x = 262,500
Therefore, we would predict that a total of 262,500 people have enjoyed the movie based on the sample of 8,000 people.