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?
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
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!
Oh I get it now! Thanks a lot! :D
Nice slamat
When we say a coin is biased in probability, it means that the coin is not evenly balanced and has a higher chance of landing on one side (head or tail) compared to the other side. In this case, the coin is biased so that a head is twice as likely to occur as a tail.
To find the probability of getting 2 tails and 1 head when the coin is tossed 3 times, we can use the concept of probability and the information about the coin's bias. Here's how you can calculate it:
First, let's find the probability of getting a head (H) and a tail (T) for the biased coin. Since the coin is twice as likely to land on heads, we can express the probabilities as follows:
P(H) = 2/3 (2 out of 3 times)
P(T) = 1/3 (1 out of 3 times)
Next, we can use the concept of combination to find the probability of getting 2 tails and 1 head in any order when tossing the coin 3 times.
There are 3 possible combinations for getting this outcome: TTH, THT, and HTT.
To find the probability of each combination, we multiply the probabilities of each individual outcome. For example, the probability of TTH is calculated as:
P(TTH) = P(T) * P(T) * P(H) = (1/3) * (1/3) * (2/3) = 2/27
Since getting 2 tails and 1 head can occur in any of the 3 possible combinations, we sum up the probabilities of all 3 combinations:
P(2T 1H) = P(TTH) + P(THT) + P(HTT) = 2/27 + 2/27 + 2/27 = 6/27 = 2/9
Therefore, the probability of getting 2 tails and 1 head when tossing the coin 3 times is 2/9 or approximately 0.2222 (rounded to four decimal places).
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!