In the following puzzles assume the coin is fair meaning it

In the following puzzles, assume the coin is fair, meaning it has a 1/2 chance of landing heads up. Assume that different coin flips are independent, meaning we can multiply the probabilities of individual events (heads up, tails up) to get the probability of the whole sequence of events. Also, assume the deck of card has no joker and is well shuffled, meaning every possible ordering of the deck is equally probable.

Question:

If I flip a coin 8 times, what is the probability that it lands heads up an odd number of times?

Can someone please explain to this to me a in a step by step solution! Thanks

Solution

Note that the probability of x successes out of n trials is

P(n, x) = nCx p^x (1 - p)^(n - x)

where

n = number of trials = 8
p = the probability of a success = 0.5
x = the number of successes

Hence, the probability distirbution below:

Thus,

P(odd) = P(1) + P(3) + P(5) + P(7) = 0.5 [ANSWER]