Answer:
J, 0.125
Answer explanation:
The probability of getting heads on any given flip of a fair, two-sided coin is 1/2. Similarly, the probability of getting tails on any given flip is also 1/2.
Assuming that the coin is fair and each flip is independent of the others, the probability of getting a specific sequence of heads and tails is found by multiplying the probabilities of each individual flip.
In this case, the probability of getting heads on the first flip is 1/2, the probability of getting tails on the second flip is also 1/2, and the probability of getting tails on the third flip is also 1/2. Therefore, the probability of getting the sequence "heads on the first flip, tails on the second flip, and tails on the third flip" is:
1/2 x 1/2 x 1/2 = 1/8 = 0.125
So the answer is option J, 0.125.
Step-by-step explanation:
The probability of getting a specific sequence of outcomes when flipping a fair coin multiple times is found by multiplying the probabilities of each individual outcome. This is because each flip is independent of the others, meaning that the outcome of one flip does not affect the outcome of any other flip.
In this case, we want to find the probability of getting a specific sequence of outcomes: heads on the first flip, tails on the second flip, and tails on the third flip.
The probability of getting heads on the first flip is 1/2, since there are two equally likely outcomes (heads or tails) and we are assuming a fair coin.
The probability of getting tails on the second flip is also 1/2, since each flip is independent of the others and the probability of getting tails on any given flip is 1/2.
The probability of getting tails on the third flip is likewise 1/2.
Therefore, the overall probability of getting this specific sequence of outcomes is found by multiplying the individual probabilities together:
P(heads on the first flip AND tails on the second flip AND tails on the third flip) = P(heads on the first flip) x P(tails on the second flip) x P(tails on the third flip)
= 1/2 x 1/2 x 1/2 = 1/8 = 0.125
So the probability of getting the desired sequence is 0.125, or 12.5%.
Easier explanation:
The probability of an event happening is the number of ways that event can happen divided by the total number of possible outcomes.
In this problem, there are 2 possible outcomes for each coin flip: heads or tails. Since the coin is flipped 3 times, there are a total of 2^3 = 8 possible outcomes (2 outcomes for each flip, and 3 flips in total).
The probability of getting heads on the first flip is 1/2, since there is only one way to get heads out of two possible outcomes (heads or tails). Similarly, the probability of getting tails on the second flip is also 1/2, and the probability of getting tails on the third flip is also 1/2.
To find the probability of all three events happening, we need to multiply their individual probabilities. So the probability of getting heads on the first flip AND tails on the second flip AND tails on the third flip is:
1/2 x 1/2 x 1/2 = 1/8
So the answer is J, 0.125.
Hope this helps! I'm sorry if it doesn't. If you need more help, or need more help explaining this, ask me! :]