You roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 4 and flipping tails? Write your answer as a fraction in simplest form.
The probability is
1/12.
There are two events that need to occur: rolling a number greater than 4 and flipping tails.
First, let's find the probability of rolling a number greater than 4. The number cube has 6 sides, and two of them have a number greater than 4 - 5 and 6. So the probability of rolling a number greater than 4 is 2/6 or 1/3.
Next, let's find the probability of flipping tails. The coin has two sides, so the probability of flipping tails is 1/2.
To find the probability of both events occurring, we multiply the probability of rolling a number greater than 4 and the probability of flipping tails:
1/3 x 1/2 = 1/6
So the probability of rolling a number greater than 4 and flipping tails is 1/6. However, the question asks for the probability of rolling a number greater than 4 and flipping tails, which means we are only considering situations where both events occur.
Out of the 6 possible outcomes of rolling the number cube and flipping the coin, only one satisfies both conditions: rolling a 5 and flipping tails. So there is only 1 way out of 6 possible outcomes for both events to occur.
Therefore, the probability of rolling a number greater than 4 and flipping tails is 1/6.
what is the answer tooYou roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 3 and flipping heads? Write your answer as a fraction in simplest form.
The probability is
1/4.
To roll a number greater than 3 on a six-sided number cube, there are 3 possible outcomes: rolling a 4, 5, or 6. Since every side of a fair die has an equal probability of landing face-up, the probability of rolling a number greater than 3 is 3/6 or 1/2.
To flip heads on a coin, there are 2 possible outcomes: heads or tails. Since again, every side of a fair coin has an equal probability of landing face-up, the probability of flipping heads is 1/2.
To find the probability of both events occurring, we multiply the probability of rolling a number greater than 3 and the probability of flipping heads:
1/2 x 1/2 = 1/4
So the probability of rolling a number greater than 3 and flipping heads is 1/4.
whats the answer tooYou spin the spinner, flip a coin, and spin the spinner again. Find the probability of spinning an odd number, flipping heads, and then spinning an even number.
Assuming the spinner has an equal chance of landing on each section, there are several ways to approach this problem. One method is to multiply the probabilities of each event occurring:
- The probability of spinning an odd number is 3/8, since there are three odd numbers out of eight total sections.
- The probability of flipping heads is 1/2, since there are two equally likely outcomes.
- The probability of spinning an even number is 5/8, since there are five even numbers out of eight total sections.
Multiplying these probabilities together, we get:
3/8 x 1/2 x 5/8 = 15/256
Therefore, the probability of spinning an odd number, flipping heads, and then spinning an even number is 15/256.
answer tooYou choose two different movies on a list at random. Out of 7 movies on the list, 3 are action movies. The first movie you choose is an action movie. What is the probability that the second movie is also an action movie? Write your answer as a fraction in simplest form.
The probability is
2/6 or 1/3.
Since the first movie chosen is an action movie, there are now only 6 movies left to choose from, and 2 of them are action movies. So the probability of choosing a second action movie is 2/6 or 1/3.
Alternatively, we can use conditional probability to solve this problem. We want to find the probability of choosing an action movie for the second pick, given that we already know the first pick was an action movie. We can use the formula for conditional probability:
P(A | B) = P(A and B) / P(B)
Here, A represents choosing an action movie for the second pick, and B represents choosing an action movie for the first pick.
The probability of choosing an action movie for the first pick is 3/7. The probability of choosing an action movie for the second pick, given that the first pick was an action movie, is 2/6 (since there are two action movies left out of a total of 6 movies remaining).
Using the formula above, we can calculate:
P(A | B) = (3/7) x (2/6) / (3/7) = 2/6
Therefore, the probability of choosing an action movie for the second pick, given that the first pick was an action movie, is 2/6 or 1/3.