Questions: A fair coin is flipped 14 times. Find the probability that more than 7 of the flips turn up tails. 0.395264 0.366254 0.424859 0.258637 0.337966 0.454896

A fair coin is flipped 14 times. Find the probability that more than 7 of the flips turn up tails.
0.395264
0.366254
0.424859
0.258637
0.337966
0.454896

Transcript text: A fair coin is flipped 14 times. Find the probability that more than 7 of the flips turn up tails. 0.395264 0.366254 0.424859 0.258637 0.337966 0.454896

Solution

Solution Steps

Step 1: Calculate the Total Possible Outcomes

For 14 flips of a fair coin, there are \(2^14 = 16384\) total possible outcomes.

Step 2: Calculate the Number of Favorable Outcomes

To find the number of outcomes with more than \(X\) tails, we calculate the number of outcomes for each possible number of tails greater than \(X\) and sum them up. This is done using the binomial coefficient \(inom{N}{k} = \frac{N!}{k!(N-k)!}\), where \(k\) is the number of tails.

Step 3: Sum the Probabilities

The probability of having more than \(X\) tails out of \(N\) flips is calculated by summing up the probabilities for having \(X+1\) to \(N\) tails.

Step 4: Calculate the Probability

The probability of having more than \(X\) tails when flipping a fair coin \(N\) times is \(0.395\).