Continue the flipping of a fair coin 100 times Calculate th

%) Continue the flipping of a fair coin 100 times.

Calculate the probability of at least 50 heads with up to 4 significant digits.

(6%) Directly like you what you did in week 1 or week 2 using combinatorics.

(6%) Approximately using De Moivre-Laplace formula like in (6.93). Note you can approximate F(n) if n > 4.99 (not in table 3.1 or 3.2) since we are only interested in 4 significant digits.

Solution

A.

We use binomial distirbution here.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    100      
p = the probability of a success =    0.5      
x = our critical value of successes =    50      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   49   ) =    0.460205381
          
Thus, the probability of at least   50   successes is  
          
P(at least   50   ) =    0.539794619 [ANSWER]

*********************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Thanks!