Question

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, what is the probability of getting 2 tails and 1 head?

What do you mean by biased in probability?

Answer 1

Well,It all depends on how hard you're flipping the coin. So, if you barley flip it, it will not flip as much, and if you flip it hard, it will flip much more.

h=2/3, t=1/3
(h+t)^3
nCr=3C2=3
3ht^2
= 3 * 2/3 * (1/3)^2
=2/9 the probability of getting 2 tails and 1 head.

Hope this helps!

Answer 2

How did it become 2/3? Does the 3 refer to the number of toss? And the 2 refer to the occurrence of the head?

I'm sorry if I ask too many questions. Thank you for helping me!

Answer 3

let prob(tail) = x
let prob(heads) = 2x , (it said so in the question)

but x + 2x = 1
x = 1/3
prob(tails) = x = 1/3
prob(heads) = 2x = 2/3

prob(exactly 2 out of 3 tails)
= C(3,2) (1/3)^2 (2/3)
= 2/9

Answer 4

Oh I get it now! Thanks a lot! :D

Answer 5

Nice slamat