1)You roll a 6-sided number cube twice. Find P(3, then even). Write the probability as a fraction in simplest form.
2)Sasha visits the ice cream parlor and asks the server to randomly choose her bowl color, ice cream flavor, and topping for her. Use the chart above to determine the probability that she will get a pink bowl with chocolate ice cream and sprinkles.
3)A 6-sided number cube is rolled 300 times. The number 5 comes up 44 times.
a. What is the theoretical probability of rolling a 5? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 5? Write your answer as a fraction in simplest form.
4)Lexi works in a bakery that bakes 500 cakes each day. When 20 cakes were cut, it was discovered that 3 of them had uneven cake layers. Estimate how many cakes have uneven layers each day
5)The probability of winning a game is 10%. How many times should you expect to win if you play 50 times?
6)A 6-sided number cube is is tossed. What is the probability of rolling an even number?
(Can you please help me ? I would love if you just give me the steps and let me figure it out on my own 😊✌🏾👇🏾)
-Q&J Wiiffeyy❤
Of course! I'd be happy to help you with these questions. Here are the steps to solve each problem, along with some explanations to help you understand the process:
1) To find the probability of rolling a 3 first and then an even number, we need to determine the number of favorable outcomes and the total number of possible outcomes.
- The number cube has 6 sides, so the total number of possible outcomes for each roll is 6.
- Since we want to roll a 3 first and an even number second, there is only 1 favorable outcome for the first roll (rolling a 3) and 3 favorable outcomes for the second roll (rolling a 2, 4, or 6).
- Multiply the number of favorable outcomes from each roll: 1 * 3 = 3.
- Multiply the total number of possible outcomes from each roll: 6 * 6 = 36.
Therefore, the probability of rolling a 3 first and then an even number is 3/36, which simplifies to 1/12.
2) To determine the probability of getting a pink bowl with chocolate ice cream and sprinkles, we need to use the given chart.
- Find the probability of choosing a pink bowl first. Look for the row corresponding to the color of the bowl and find the number in the chart divided by the total number of options. Let's say the probability is 1/5.
- Find the probability of choosing chocolate ice cream next. Again, find the row corresponding to the ice cream flavor and divide the number in the chart by the total number of options. Let's say the probability is 1/4.
- Finally, find the probability of choosing sprinkles. Follow the same process by finding the row for the topping and dividing the number in the chart by the total number of options. Let's say the probability is 1/3.
To find the overall probability, multiply the probabilities of each event together: (1/5) * (1/4) * (1/3) = 1/60.
So, the probability of Sasha getting a pink bowl with chocolate ice cream and sprinkles is 1/60.
3) a. The theoretical probability of rolling a number on a fair 6-sided number cube is determined by dividing the number of favorable outcomes (getting a 5) by the total number of possible outcomes.
- There are 6 possible outcomes when rolling a number cube (numbers 1 to 6).
- There is only 1 favorable outcome (getting a 5).
The theoretical probability of rolling a 5 is 1/6.
b. The experimental probability of rolling a 5 is calculated by dividing the number of favorable outcomes (the number of times a 5 comes up) by the total number of trials (the number of times the cube is rolled).
- In this case, the number of times a 5 comes up is given as 44.
- The total number of trials is given as 300.
The experimental probability of rolling a 5 is 44/300, which can be simplified further if needed.
4) To estimate the number of cakes with uneven layers each day, we can use the proportion of cakes with uneven layers found in the sample of 20 cakes.
- The proportion of cakes with uneven layers is 3/20.
- Apply this proportion to the total number of cakes baked each day, which is 500.
Multiply the proportion by the total number of cakes: (3/20) * 500 = 75.
Therefore, an estimated 75 cakes have uneven layers each day.
5) To determine the number of times you should expect to win if you play 50 times, we can use the probability of winning the game.
- The probability of winning is given as 10%, which can also be written as 10/100 or 1/10.
- Multiply this probability by the number of times you play the game: (1/10) * 50 = 5.
Therefore, you should expect to win 5 times if you play 50 times.
6) The probability of rolling an even number on a 6-sided number cube can be found by determining the number of favorable outcomes (rolling a 2, 4, or 6) and dividing it by the total number of possible outcomes (numbers 1 to 6).
- There are 3 favorable outcomes (2, 4, and 6).
- The total number of possible outcomes is 6.
So, the probability of rolling an even number is 3/6, which simplifies to 1/2.
I hope this helps! Let me know if you have any more questions.