A student has a bag of marbles. There are 5 pink, 7 red, 12 green, 2 blue, and 4 black marbles in the bag. Calculate the theoretical probability of picking a green marble.(1 point)
The total number of marbles in the bag is 5 (pink) + 7 (red) + 12 (green) + 2 (blue) + 4 (black) = 30 marbles.
The theoretical probability of picking a green marble can be calculated as:
Number of favorable outcomes (green marbles) / Total number of possible outcomes = 12 / 30 = 2 / 5
Therefore, the theoretical probability of picking a green marble is 2/5 or 0.4.
Emma has a bag of marbles. There are 9 pink, 5 red, 8 green, 2 blue, and 6 white marbles in the bag. Calculate the complement of not picking a pink marble.(1 point)
The total number of marbles in the bag is 9 (pink) + 5 (red) + 8 (green) + 2 (blue) + 6 (white) = 30 marbles.
The probability of not picking a pink marble can be calculated as:
Number of favorable outcomes (not picking a pink marble) = Total number of marbles - Number of pink marbles = 30 - 9 = 21
Probability of not picking a pink marble = Number of favorable outcomes / Total number of possible outcomes = 21 / 30 = 7 / 10
The complement of not picking a pink marble (picking a pink marble) = 1 - Probability of not picking a pink marble
= 1 - 7/10
= 3/10
Therefore, the complement of not picking a pink marble is 3/10 or 0.3.
A spinner with 9 equal sections labeled with the letters A, A, B, B, B, C, C, C, and D is spun 198 times. Which of the following correctly predicts how many times the spinner will land on the letter B?(1 point)
The probability of landing on each letter can be calculated based on the number of sections labeled with that letter out of the total 9 sections:
- P(A) = 2/9
- P(B) = 3/9 = 1/3
- P(C) = 3/9 = 1/3
- P(D) = 1/9
Since the probability of landing on B is 1/3, we can predict the number of times the spinner will land on B by multiplying the probability by the total number of spins:
Number of times landing on B = Probability of landing on B x Total number of spins
= (1/3) x 198
= 198 / 3
= 66
Therefore, the spinner is predicted to land on the letter B 66 times out of 198 spins.
Conor has a bag of marbles. He counts out 10 marbles and finds that there are 3 blue marbles among them. If the bag has 600 marbles, predict how many will be blue.(1 point)
If Conor has counted 10 marbles and found 3 of them to be blue, we can calculate the proportion of blue marbles in the sample:
Proportion of blue marbles in the sample = Number of blue marbles in the sample / Total number of marbles in the sample = 3 / 10 = 0.3
Since the sample represents the total bag of 600 marbles, we can use this proportion to predict the total number of blue marbles in the bag:
Predicted number of blue marbles in the bag = Proportion of blue marbles in the sample x Total number of marbles in the bag
= 0.3 x 600
= 180
Therefore, it is predicted that there will be 180 blue marbles in the bag.
A student demonstrates probability by using a 6-sided number cube with numbers 1, 2, 3, 4, 5, and 6. The student rolls the number cube 246 times. Predict how many times a 3 or 5 will be rolled.(1 point)
To predict how many times a 3 or 5 will be rolled on a 6-sided number cube over 246 rolls, we first calculate the probability of rolling a 3 or a 5.
There are a total of 6 possible outcomes (numbers 1 to 6) on a 6-sided number cube.
Number of favorable outcomes (rolling a 3 or a 5) = 2 (numbers 3 and 5)
Total number of possible outcomes = 6
The probability of rolling a 3 or a 5 is:
P(rolling a 3 or 5) = Number of favorable outcomes / Total number of possible outcomes
= 2 / 6
= 1 / 3
To predict how many times a 3 or 5 will be rolled out of 246 rolls, we multiply the probability by the total number of rolls:
Predicted number of times rolling a 3 or 5 = (1 / 3) x 246
= 82
Therefore, it is predicted that a 3 or 5 will be rolled approximately 82 times out of 246 rolls.