A bag contains 4 white, 3 blue, and 5 red marbles.
1. Find the probability of choosing a red marble, then a white marble if the marbles are replaced. (1 point)
one-twelfth
five over thirty-six
five-sixths
five-twelfths
A bag contains 4 white, 3 blue, and 5 red marbles.
2. Find the probability of choosing 3 blue marbles in a row if the marbles are replaced. (1 point)
two over eleven
one over two hundred twenty
Fraction 1 over 27 end fraction
one over sixty-four
A bag contains 4 white, 3 blue, and 5 red marbles.
3. Find the probability of choosing a blue marble, then a red marble if the marbles are not replaced. (1 point)
five over forty-four
fifteen over thirty-five
two-thirds
one over fifteen
A bag contains 4 white, 3 blue, and 5 red marbles.
4. Find the probability of choosing 2 white marbles in a row if the marbles are not replaced. (1 point)
The fraction states 1 over 11.
one-ninth
two-thirds
Start Fraction 1 over 16 End Fraction
A bag contains 4 white, 3 blue, and 5 red marbles.
1. Probability of choosing a red marble, then a white marble with replacement = probability of choosing a red marble * probability of choosing a white marble = (5/12)*(4/12) = 5/36. Answer: B. five over thirty-six
2. Probability of choosing 3 blue marbles in a row with replacement = probability of choosing a blue marble * probability of choosing another blue marble * probability of choosing another blue marble = (3/12)*(3/12)*(3/12) = 1/64. Answer: D. one over sixty-four
3. Probability of choosing a blue marble, then a red marble without replacement = probability of choosing a blue marble * probability of choosing a red marble from remaining marbles = (3/12)*(5/11) = 15/132 = 5/44. Answer: A. five over forty-four
4. Probability of choosing 2 white marbles in a row without replacement = probability of choosing a white marble * probability of choosing another white marble from remaining marbles = (4/12)*(3/11) = 1/11. Answer: A. the fraction states 1 over 11.
Bot is correct.
Thank you!
To solve these probability problems, we need to determine the number of favorable outcomes (the desired marble sequence) and the number of total outcomes (the total number of marbles).
1. Probability of choosing a red marble, then a white marble with replacement:
The probability of choosing a red marble is 5/12 since there are 5 red marbles out of a total of 12 marbles. Similarly, the probability of choosing a white marble is 4/12 since there are 4 white marbles out of a total of 12 marbles. Since the marbles are replaced, the outcomes are independent, so we can multiply the probabilities together:
P(choosing a red marble, then a white marble) = (5/12) * (4/12) = 20/144 = 5/36
2. Probability of choosing 3 blue marbles in a row with replacement:
The probability of choosing a blue marble is 3/12 (since there are 3 blue marbles out of 12 marbles) and since the marbles are replaced, the probabilities remain the same for each draw. Again, the outcomes are independent, so we can multiply the probabilities together:
P(choosing 3 blue marbles in a row) = (3/12)^3 = 27/1728 = 1/64
3. Probability of choosing a blue marble, then a red marble without replacement:
The probability of choosing a blue marble is 3/12, and after removing 1 blue marble, we have 11 marbles left in the bag, one of which is red. So the probability of choosing a red marble after a blue marble has been chosen is 1/11. Again, the outcomes are independent, so we can multiply the probabilities together:
P(choosing a blue marble, then a red marble) = (3/12) * (1/11) = 3/132 = 1/44
4. Probability of choosing 2 white marbles in a row without replacement:
The probability of choosing the first white marble is 4/12, and after removing 1 white marble, we have 11 marbles left in the bag, 3 of which are white. So the probability of choosing a second white marble after the first white marble has been chosen is 3/11. Again, the outcomes are independent, so we can multiply the probabilities together:
P(choosing 2 white marbles in a row) = (4/12) * (3/11) = 12/132 = 1/11
Therefore, the answers to the given probabilities are:
1. Five-twelfths
2. One over sixty-four
3. One over forty-four
4. The fraction is 1 over 11.