#6c
nflips = 50
ntrials = 10000
total = 0 # We’ll keep a running total of all the trials’ longest runs
for (j in 1:ntrials)
{
    # One trial consists of 50 flips
    trial = rbinom(nflips, 1, .5) # binomial(1,.5) = bernoulli(.5)
    # rle() finds the lengths of all the runs in trials. We add the max to total
    total = total + max(rle(trial)$lengths)
}
# The average maximum run is the total/ntrials
aveMax = total/ntrials 
aveMax


#6d
nflips = 50
ntrials = 10000
# We’ll keep a running cnt of all the trials with a run of 8 or more
count = 0
for (j in 1:ntrials)
{
    trial = rbinom(nflips, 1, .5) # binomial(1,.5) = bernoulli(.5)
    count = count + (max(rle(trial)$lengths) >= 8)
}
# The probability of a run of 8 or more is count/ntrials
prob8 = count/ntrials
prob8