Calculate the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes from a single toss
There are a total of 36 possible outcomes when rolling a pair of number cubes (each cube has 6 faces, so there are 6 * 6 = 36 possible combinations).
To calculate the theoretical probability of rolling a total of 7 or 11, we first need to determine the number of ways to get each sum:
1. Total of 7:
- (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) - 6 ways
2. Total of 11:
- (5,6), (6,5) - 2 ways
Adding the number of ways to get a total of 7 or 11, we get a total of 6 + 2 = 8 favorable outcomes.
Therefore, the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes from a single toss is 8/36, which simplifies to 2/9 or approximately 0.2222 or 22.22%.
A six sided number cube is rolled 30 times and land on 3 ten times and on 5 eight times. Calculate the experimental probability of landing on a 3. Write your answer in the simplest form of a fraction
To calculate the experimental probability of landing on a 3 when rolling the number cube 30 times, you first need to determine the total number of times the cube landed on a 3.
Since the cube landed on 3 ten times out of 30 total rolls, the experimental probability of landing on a 3 is 10/30, which simplifies to 1/3.
Therefore, the experimental probability of landing on a 3 when rolling the number cube 30 times is 1/3.
The experiment involved tossing three coins simultaneously. The experiment was carried out 100 times, and it was noted that three heads occurred 40 times. What is the difference between the experimental probability of getting three heads and its theoretical probability. Write the answer in the simplest form of fraction
When three coins are tossed simultaneously, there are a total of 2^3 = 8 possible outcomes (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).
The theoretical probability of getting three heads (HHH) in a single toss is 1/8, as there is only one favorable outcome out of the total 8 possible outcomes.
Given that the experiment was carried out 100 times and three heads occurred 40 times, we can calculate the experimental probability of getting three heads as 40/100, which simplifies to 2/5.
The difference between the experimental probability and the theoretical probability is:
Experimental Probability - Theoretical Probability
= 2/5 - 1/8
= 16/40 - 5/40
= 11/40
Therefore, the difference between the experimental probability of getting three heads and its theoretical probability is 11/40.
An experiment involves picking cars from the number cards 2, 4,6,10. In equation form, what is the probability model for this experiment
f (x) = (blank), where x = 2,4,6,10
In this experiment, the probability model represents the likelihood of picking each number card from the set {2, 4, 6, 10}. Since each card has an equal probability of being picked, the probability model can be written as:
f(x) = 1/4 for x = 2, 4, 6, 10
This equation indicates that the probability of picking any of the cards (2, 4, 6, or 10) is 1/4 for each card selected.
Suppose the probability of selecting a supermarket shopper who prefers plastic bags instead of paper badges is 50% out of 150 shoppers how many can you expect will order plastic bags
If the probability of selecting a supermarket shopper who prefers plastic bags instead of paper bags is 50% or 0.5, and there are 150 shoppers in total, you can expect that 0.5 * 150 = 75 shoppers will order plastic bags.
Therefore, you can expect 75 shoppers out of the 150 total shoppers to order plastic bags.