I know its 1 - P(5/128) but I don't think its correct??
I flip a fair coin seven times in a row. What is the probability that I get at most five heads?
To find the probability of getting at most five heads when flipping a fair coin seven times, we can calculate the probability of getting zero, one, two, three, four, or five heads and then sum them up.
The probability of getting zero heads is the same as getting seven tails, which is (1/2) raised to the power of 7 (since there are 2 possible outcomes for each coin flip).
The probability of getting one head is the same as getting six tails and one head. There are 7 different positions where the head can occur (first flip, second flip, etc.), so we multiply the probability of getting a head (1/2) by the probability of getting six tails (1/2) raised to the power of 6.
Similarly, we can calculate the probabilities for two, three, four, and five heads.
To calculate the probability of getting two heads, we multiply the probability of getting two heads (1/2) squared by the probability of getting five tails (1/2) raised to the power of 5.
To calculate the probability of getting three heads, we multiply the probability of getting three heads (1/2) cubed by the probability of getting four tails (1/2) raised to the power of 4.
To calculate the probability of getting four heads, we multiply the probability of getting four heads (1/2) to the power of 4 by the probability of getting three tails (1/2) raised to the power of 3.
To calculate the probability of getting five heads, we multiply the probability of getting five heads (1/2) to the power of 5 by the probability of getting two tails (1/2) squared.
Finally, we add up all these probabilities to get the probability of getting at most five heads:
P(at most 5 heads) = P(0 heads) + P(1 head) + P(2 heads) + P(3 heads) + P(4 heads) + P(5 heads)
Calculating the individual probabilities and summing them up will give you the correct answer.