A basket of fruits contains five apples and three pairs. Sharon took two fruits at random. What is the probability that both fruits are apples? Write your answer in the simplest form of a fraction.
There are a total of 8 fruits in the basket. The probability of choosing an apple on the first try is 5/8, since there are 5 apples out of 8 fruits. After taking one fruit out, there are 7 fruits left, out of which there are 4 apples. Therefore, the probability of choosing another apple on the second try is 4/7. To find the probability of both events happening, we multiply the probabilities:
P(both fruits are apples) = (5/8) x (4/7)
Simplifying this fraction, we get:
P(both fruits are apples) = 20/56
This fraction can be reduced further by dividing both the numerator and denominator by 4:
P(both fruits are apples) = 5/14
Therefore, the probability that both fruits are apples is 5/14.
A coin is flipped in a spinner is spun simultaneously. The spinner is divided into six equal size sections labeled with one, two, three, four, five, six. What is the probability of flipping a tail and landing on five?
The coin flip and spinner spin are independent events, meaning that one does not affect the other.
The probability of flipping a tail is 1/2, since there are two equally likely outcomes (heads and tails) and one of them is a tail.
The probability of landing on five on the spinner is 1/6, since the spinner is divided into six equal sections and only one of them is labeled with five.
To find the probability of both events happening, we multiply the probabilities:
P(tail and landing on five) = (1/2) x (1/6)
Simplifying this product, we get:
P(tail and landing on five) = 1/12
Therefore, the probability of flipping a tail and landing on five is 1/12.
If two events are independent, the probability of both events occurring is the product of their individual probability. Events A and B are independent with P(A) = 0.3 and P(B) =0.25. What is the probability of events A and B happening at the same time? Write your answer in decimal form.
The probability of both independent events occurring is the product of their individual probabilities.
P(A and B) = P(A) x P(B)
Substituting the given probabilities, we get:
P(A and B) = 0.3 x 0.25
Simplifying this product, we get:
P(A and B) = 0.075
Therefore, the probability of events A and B happening at the same time is 0.075, or 7.5% as a decimal.
A spinner labeled with the letters of the word HONEST is to be spun once. Describe the probability of landing on an H, S, or E.
There are six letters in the word HONEST, so the spinner has six sections, each labeled with a different letter.
To find the probability of landing on an H, S, or E, we need to first count the number of sections that have an H, S, or E label.
There is one H, one S, and two Es in the word HONEST, so there are a total of four sections with an H, S, or E label.
Therefore, the probability of landing on an H, S, or E is 4/6 or 2/3 (in simplest form).
Which set of events is dependent?
1. Rolling a Number cube and flipping a coin
2. The event of getting two heads when flipping to fair coins
3. Choosing a ball from a bag then choosing another ball without replacing the first
4. Choosing a marble from a box, replacing it, then choosing another marble
The set of events that is dependent is 3.
In this case, the second event is affected by the outcome of the first event, since the first ball is not replaced before choosing the second ball. This means that the probability of the second event depends on what happened during the first event.
In contrast, the other sets of events are independent:
1. The act of rolling a number cube has no effect on the outcome of flipping a coin, and vice versa.
2. The outcomes of the two coin flips are also independent of each other.
4. The act of replacing the marble after the first draw means that the probability of the second event remains the same, regardless of what happened during the first event.