A spinner labeled with the letters HONEST is to be spun once. Describe the probability of landing on a un-shaded section in the sample space.
a. 1/3
b. 1/2
c. 1/6
d. 3
c. 1/6
There are six letters on the spinner labeled with H, O, N, E, S, T. Only one of these letters is un-shaded, which is the letter E. Therefore, the probability of landing on a un-shaded section (the letter E) is 1 out of 6 possibilities, which corresponds to a probability of 1/6.
Which set of events is dependent?
a. choosing a marble from a box, then replacing it then choosing another marble.
b. choosing a ball from a bag and then choosing another ball without replacing the first.
c. the event of getting two heads when flipping two fair coins.
d. rolling a number cube and flipping a coin.
b. choosing a ball from a bag and then choosing another ball without replacing the first.
The events in option b are dependent because the outcome of the first choice affects the probabilities of the second choice. If the first ball is not replaced, the number of balls in the bag changes for the second choice, which impacts the probabilities of selecting different balls in the two choices.
A basket of fruits contains 5 bananas, 8 mangoes, 7 apples. Two fruits are randomly selected without replacement. Calculate the probability of selecting an apple and a banana.
a. 21/190
b. 7/76
c. 7/80
d. 3/5
The total number of fruits in the basket is 5 + 8 + 7 = 20.
The probability of selecting an apple first is 7/20.
After selecting an apple, there are 19 fruits remaining in the basket, with 5 bananas remaining. The probability of selecting a banana second, given that an apple was selected first, is 5/19.
Therefore, the probability of selecting an apple and a banana is (7/20) * (5/19) = 35/380 = 7/76.
So, the correct answer is b. 7/76.
A basket of fruits contains 10 bananas, 5 mangoes, 5 apples. Two fruits are randomly selected. Calculate the probability of selecting an apple and a banana. Express the answer in percent form.
a. 12.5%
b. 75%
c. 0
d. 62.5%
The total number of fruits in the basket is 10 (bananas) + 5 (mangoes) + 5 (apples) = 20 fruits.
The probability of selecting an apple first is 5/20 = 1/4.
After selecting an apple, there are 19 fruits remaining in the basket, with 10 bananas remaining. The probability of selecting a banana second, given that an apple was selected first, is 10/19.
Therefore, the probability of selecting an apple and a banana is (1/4) * (10/19) = 10/76.
To express this as a percentage, we have: (10/76) * 100% ≈ 13.16%.
Therefore, the closest answer is a. 12.5%.
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 the studying online or is a boy?
a. 13/25 + 10/25
b. 3/25
c. 13/25 + 10/25 - 3/25
d. 13/25 x 10/25
c. 13/25 + 10/25 - 3/25
To calculate the probability of selecting a student who wants the option to keep studying online or is a boy, you would need to consider the sum of the students who want to study online (13) and the number of boys (10), but subtract the students who are both boys and want to study online (3) to avoid double counting.
This can be represented by the mathematical sentence 13/25 + 10/25 - 3/25.
Therefore, the answer is c. 13/25 + 10/25 - 3/25.