You flip 3 coins. Is the probability of obtaining 2 heads and 1 tail in any order the same as the probability of obtaining a head, than a head then a tale?

the probability of obtaining 2 heads and 1 tail in any order is higher than the probability of obtaining a head, than a head then a tail

Step-by-step explanation:

since the probability (p) of obtaining 2 head and 1 tail in any order is

P1 = p of obtaining (H, H, T) + p of obtaining (H, T, H) + p of obtaining (T, H, H) = 3*p of obtaining (H, T, H)

assuming a fair coin then p heads = p tails = 0.5

thus since each flip is independent from the others

p (H, H, T) = p (H, T, H) = p (T, H, H) = P=0.5*0.5*0.5 = 1/8

thus P1 = 3*1/8=3/8

while the probability of obtaining a head, than a head then a tail is

P2 = p of obtaining (H, T, H) = 1/8

then P1=3/8 >P2=1 (8

therefore the probability of obtaining 2 heads and 1 tail in any order is higher than the probability of obtaining a head, than a head then a tail