A coin is flipped 7 times, what is the probability that the next flip will be tails
How do I do this?
a- 1/1
b- 1/7
c- 1/8
d- 1/2
1/7?
Each time you flip it, the coin either comes up heads or tails. There are only those two possibilities.
so 1/1?
No. You're looking for an expression that means there's one chance out of two chances.
To calculate the probability of the next flip being tails, we need to consider the number of possible outcomes that result in tails compared to the total number of possible outcomes.
In each individual coin flip, there are two possible outcomes: heads or tails. Since the coin is flipped 7 times, the total number of possible outcomes for those 7 flips is 2^7 or 128.
Now, since we are interested in the probability of the next flip being tails, we need to determine how many of those 128 outcomes would result in tails on the next flip. Because the previous 7 flips do not impact the outcome of the next flip (assuming a fair coin), each flip is independent, and there is an equal chance of getting heads or tails.
Therefore, out of the 128 possible outcomes, there are 64 outcomes that result in tails on the next flip (as the coin has an equal chance of landing on either side).
The probability of the next flip being tails is the number of outcomes that result in tails divided by the total number of possible outcomes: 64/128, which simplifies to 1/2.
So, the answer is d- 1/2