Erik is performing a marble experiment in math class. His teacher places an equal number of black, red, and white marbles in a bag. Then, Erik randomly takes out a marble, records the result, and puts the marble back in the bag. Each of the first four times Erik takes out a marble, he gets a black marble.
A. What is the theoretical probability of Erik picking a black marble next time? Based on Erik's results, what is the experimental probability of Erik picking a black marble next time?
B. Explain the difference between the two probabilities you found in part A.
C. What is the theoretical probability and likelihood of getting four black marbles in a row?
Make sure to show all your work.
A. 1/3, 1/3
B. From the way you posted it, no difference.
It would help if you would proofread your work before you post it.
C. (1/3)^4
A. The theoretical probability of picking a black marble next time can be calculated by dividing the number of favorable outcomes (getting a black marble) by the total number of possible outcomes. Since there were an equal number of black, red, and white marbles in the bag initially, the number of favorable outcomes is still the same as the initial number of black marbles. Let's assume there were n marbles of each color initially.
There were 4 favorable outcomes (getting a black marble) in the first four picks. The total number of picks is 4. Therefore, the probability of picking a black marble next time can be calculated as 4/4 = 1.
The experimental probability of Erik picking a black marble next time is based on the actual results he has obtained so far. In the first four picks, he got four black marbles. Since each time a marble is picked, recorded, and put back in the bag, the probability remains the same for each pick. Therefore, based on Erik's results, the experimental probability of picking a black marble next time is 1.
B. The difference between the two probabilities is that the theoretical probability is based on the assumption that all marbles are equally likely to be picked, while the experimental probability is based on the actual results obtained by Erik. The theoretical probability represents the likelihood of an event based on theoretical calculations, while the experimental probability represents the observed likelihood of an event based on actual experiments or observations.
C. The theoretical probability of getting four black marbles in a row can be calculated by multiplying the individual probabilities of getting a black marble in each pick. Since there were an equal number of black, red, and white marbles initially, and each pick is independent, the probability of getting a black marble in each pick is 1/n, where n is the initial number of marbles of each color.
Therefore, the theoretical probability of getting four black marbles in a row can be calculated as (1/n) * (1/n) * (1/n) * (1/n) = 1/n^4.
The likelihood of getting four black marbles in a row can be determined by knowing the total number of marbles initially. If we know the initial number of marbles, we can substitute that value into the expression 1/n^4 to calculate the likelihood. However, without knowing the initial number of marbles, we cannot determine the exact numerical value of the likelihood.
A. To find the theoretical probability, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, Erik has picked out four black marbles in a row, so the number of favorable outcomes is 1. Since there are equal numbers of black, red, and white marbles in the bag, the total number of possible outcomes is the sum of these three, which is 3.
Therefore, the theoretical probability of Erik picking a black marble next time is 1/3.
For the experimental probability, we consider the actual outcomes that Erik obtained. Since he picked out four black marbles in a row, we have 4 favorable outcomes out of the 4 trials he performed. Hence, the experimental probability of Erik picking a black marble next time is 4/4, which simplifies to 1.
B. The difference between the two probabilities is that the theoretical probability is based on the assumption of equally likely outcomes, while the experimental probability is based on the actual outcomes observed in Erik's experiment. The theoretical probability represents what we expect to happen in the long run, while the experimental probability represents what actually happened in a limited number of trials.
C. To find the theoretical probability and likelihood of getting four black marbles in a row, we multiply the probabilities of each individual event together. Since each time Erik picks a marble, there is a 1/3 chance of picking a black marble, the theoretical probability of getting four black marbles in a row is (1/3)^4.
Calculating this value, we find that the theoretical probability is 1/81.
The likelihood is another term for probability and represents the chances of a particular outcome occurring. In this case, the likelihood of getting four black marbles in a row is the same as the theoretical probability, which is 1/81.
A1/2-
P(black)=1/3
there's three colors and black is just one of them so you put 1 first then /3 because the denominator is going to be the amount of colors so that would be three so the answer is 1/3
A2/2-
we can assume that it will be the same as before p(black)=1/3. The reason its because there a three colors, and we know that black is one of the three colors, so therefore the answer is 1/3.
B-
the difference between the two provability's is zero(I'm assuming that by difference you mean to subtract). 1/3=0.333333333333
so 0.333333333333-0.333333333333=0
C- The theoretical probability of getting four black marbles in a row is 1/3*4 or 0.333333333333*4 which equals 4/3 or 1.33333333333