Question

the probability that a professional baseball player will get a hit is 1/3. calculate the exact probability that he will get at least 3 hits in 5 attempts

Answer 1

mmmmm

mmmmh
mmmhm
mmhmm
mhmmm
hmmmm

mmmhh
mmhmh
mhmmh
hmmmh
mmhhm
mhmhm
hmmhm
mhhmm
hmhmm
hhmmm

hhhmm
hhmhm
hmhhm
mhhhm
hhmmh
hmhmh = 10 (1*1*1*2*2/3^5)
mhhmh
hmmhh
mhmhh
mmhhh

hhhhm
hhhmh
hhmhh = 5(1*1*1*1*2/3^5)
hmhhh
mhhhh

hhhhh = 1(1*1*1*1*1/3^5)

and there is a total of 32 ways to hit and miss a ball in 5 swings

\[\frac{10}{32}\frac{4}{3^5}+\frac{5}{32}\frac{4}{3^5}\]
\[\frac{10}{32}\frac{4}{3^5}+\frac{5}{32}\frac{2}{3^5}+\frac{1}{32}\frac{1}{3^5}\]