A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number greater than 4.
A number cube is rolled 360 times and the results are recorded as follows: 41 ones, 54 twos, 62 threes, 75 fours, 33 fives, and 95 sixes. What is the experimental probability of rolling a two or a three?
From a barrel of colored marbles, you randomly select 6 blue, 4 yellow, 2 red, 3 green, and 5 purple marbles. Find the experimental probability of randomly selecting a marble that is not a yellow
A survey showed that 56% of car owners prefer four-door cars, 31% prefer two-door cars, and 13% have no preference. You ask 300 people. How many do you think will prefer four-door cars?
Sally works in a factory that produces 1,000 televisions each day. When 40 televisions were sampled, it was found that 6 were defective. Estimate how many defective televisions are made each day.
The spinner is divided into equal parts. Use a tree diagram to find the probability that the spinner will land on a consonant both times if the spinner is spun twice.
thank you
Anon no need to be a jerk, just help the person
You're welcome! Here are the explanations for each question:
1. Probability of rolling a number greater than 4:
To find the probability, we need to determine the number of favorable outcomes (rolling a number greater than 4) and the total number of possible outcomes (rolling any number on the standard number cube). In this case, the favorable outcomes are the numbers 5 and 6, so there are 2 favorable outcomes. The total number of possible outcomes is 6. Therefore, the probability of rolling a number greater than 4 is 2/6, which simplifies to 1/3.
2. Experimental probability of rolling a two or a three:
The experimental probability is determined by dividing the number of times an event occurred (rolling a two or a three) by the total number of trials (rolling the number cube 360 times). In this case, the number of times we rolled a two or a three is 54 + 62 = 116. Therefore, the experimental probability of rolling a two or a three is 116/360, which simplifies to 29/90.
3. Experimental probability of randomly selecting a marble that is not yellow:
Similar to the previous question, we need to divide the number of desired outcomes (marbles that are not yellow) by the total number of outcomes (the sum of all colored marbles). In this case, the number of marbles that are not yellow is 6 + 2 + 3 + 5 = 16. The total number of marbles is 6 + 4 + 2 + 3 + 5 = 20. Therefore, the experimental probability of randomly selecting a marble that is not yellow is 16/20, which simplifies to 4/5.
4. Number of people who prefer four-door cars:
To estimate the number of people who prefer four-door cars, we need to multiply the percentage (56%) by the total number of people (300). So, 56% of 300 is (56/100) * 300 = 168.
5. Estimate of the number of defective televisions made each day:
To estimate the number of defective televisions made each day, we need to find the ratio of defective televisions in the sample (6 out of 40) to the total production of televisions each day (1,000). Then, we can multiply this ratio by the total number of televisions produced each day. So, the estimate is (6/40) * 1000 = 150 defective televisions.
6. Probability of landing on a consonant both times using a spinner:
To find the probability, we can create a tree diagram. Assuming there are 4 possible outcomes: consonant (C), vowel (V), the probability of landing on a consonant is 2/4 = 1/2, and the probability of landing on a vowel is 2/4 = 1/2. Since we spin the spinner twice, we multiply the probabilities together. Therefore, the probability of landing on a consonant both times is (1/2) * (1/2) = 1/4.
I hope these explanations have helped you understand how to solve each problem. If you have any more questions, feel free to ask!