Which set of events is dependent?(1 point)
Responses
choosing a marble from a box, replacing it, then choosing another marble
choosing a marble from a box, replacing it, then choosing another marble
rolling a number cube and flipping a coin
rolling a number cube and flipping a coin
choosing a ball from a bag and then choosing another ball without replacing the first
choosing a ball from a bag and then choosing another ball without replacing the first
the event of getting two heads when flipping two fair coins
choosing a ball from a bag and then choosing another ball without replacing the first
A basket of fruits contains 5 bananas, 8 mangoes, and 7 apples. Two fruits are randomly selected without replacement. Calculate the probability of selecting an apple and a banana.(1 point)
Responses
To calculate the probability of selecting an apple and a banana without replacement, first calculate the total number of ways two fruits can be selected out of 20 fruits (5 bananas + 8 mangoes + 7 apples).
Total number of ways = 20C2 = (20 * 19) / (2 * 1) = 190 ways
Next, calculate the number of ways to select an apple and a banana.
Number of ways to select an apple = 7C1 = 7
Number of ways to select a banana = 5C1 = 5
Number of ways to select an apple and a banana = 7 * 5 = 35 ways
Therefore, the probability of selecting an apple and a banana is:
Probability = Number of ways to select an apple and a banana / Total number of ways
Probability = 35 / 190
Probability ≈ 0.1842 or 18.42%
A basket of fruits contains 5 bananas, 8 mangoes, and 7 apples. Two fruits are randomly selected without replacement. Calculate the probability of selecting an apple and a banana.(1 point)
Responses
35
Start Fraction 3 over 5 End Fraction
780
Start Fraction 7 over 80 End Fraction
21190
Start Fraction 21 over 190 End Fraction
776
Start Fraction 21 over 190 End Fraction
A basket of fruits contains 10 bananas, 5 mangoes, and 5 apples. A fruit is selected at random. Calculate the probability of selecting an apple or a banana. Express the answer in percent form.(1 point)
Responses
75%
75%
0
0
12.5%
12.5%
62.5%
To calculate the probability of selecting an apple or a banana, first add the number of apples and bananas:
Number of apples + Number of bananas = 5 + 10 = 15
Total number of fruits = 10 (bananas) + 5 (mangoes) + 5 (apples) = 20
Probability of selecting an apple or a banana = Number of apples + Number of bananas / Total number of fruits
Probability = 15 / 20 = 0.75 or 75%
So, the probability of selecting an apple or a banana is 75%.
Therefore, the correct answer is
75%
Use the table to answer the question.
Studying Online
Girls Boys Row total
Want the option to keep studying online 10 3 13
Don’t want the option to keep studying online 5 7 12
Column total 15 10 25
Which mathematical sentence can be used to calculate the probability of selecting a student who wants the option to keep studying online or is a boy?
(1 point)
To calculate the probability of selecting a student who wants the option to keep studying online or is a boy, use the formula for probability:
P(A or B) = P(A) + P(B) - P(A and B)
Where:
P(A or B) is the probability of selecting a student who wants the option to keep studying online or is a boy
P(A) is the probability of selecting a student who wants the option to keep studying online
P(B) is the probability of selecting a boy
P(A and B) is the probability of selecting a student who wants the option to keep studying online and is a boy
From the table:
P(A) = 13/25 (Want the option to keep studying online)
P(B) = 10/25 (Boys)
P(A and B) = 3/25 (Boys who want the option to keep studying online)
Substitute the values into the formula:
P(A or B) = 13/25 + 10/25 - 3/25
P(A or B) = 13/25 + 10/25 - 3/25
P(A or B) = 20/25
Therefore, the mathematical sentence that can be used to calculate the probability of selecting a student who wants the option to keep studying online or is a boy is:
20/25
Use the table to answer the question.
Studying Online
Girls Boys Row total
Want the option to keep studying online 10 3 13
Don’t want the option to keep studying online 5 7 12
Column total 15 10 25
Which mathematical sentence can be used to calculate the probability of selecting a student who wants the option to keep studying online or is a boy?
(1 point)
Responses
1325+1025−325
Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction
1325+1025
Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction
325
Start Fraction 3 over 25 End Fraction
1325×1025