Question: "A coin is tossed 8 times. Find the probability P(of exactly 6 occurrences of tails)"
Answer:
When we toss a coin we have 50% of probability to get a tail and 50% probability to get heads.
If we toss the coin 8 times, in order to find P(T=6), we need to use the binomial distribution:
[tex]P = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events
k = number of successes we want
p = probability of success
Therefore:
[tex]P(T=6) = \frac{8!}{6!(2)!} 0.5^{6} (1-0.5)^{2} [/tex]
= 28 · 0.015625 · 0.25
= 0.109375
Hence, the probability of getting 6 tails out of 8 tosses is D) 10.94%.
