A bent coin is tossed 5 times. the probability of tails is 2/3/ find the probability that tails will show exactly 3 times.?
回答 (4)
2016-08-01 11:41 pm
Use the binomial probability formula:
P(X = k) = C(n, k) * p^k * q^(n-k)
n : number of trials (5)
k : number of successes (3)
p : probability of success (2/3)
q : probability of failure (1-p = 1/3)
Plug in the numbers:
P(X = 3) = C(5,3) * (2/3)^3 * (1/3)^2
= 10 * 8/27 * 1/9
= 80/243
P(X = k) = C(n, k) * p^k * q^(n-k)
n : number of trials (5)
k : number of successes (3)
p : probability of success (2/3)
q : probability of failure (1-p = 1/3)
Plug in the numbers:
P(X = 3) = C(5,3) * (2/3)^3 * (1/3)^2
= 10 * 8/27 * 1/9
= 80/243
2016-08-01 11:47 pm
This is a standard binomial experiment,
with p = 2/3, # trials = 5, # successes = 3.
Now just use the formula
with p = 2/3, # trials = 5, # successes = 3.
Now just use the formula
2016-08-01 11:42 pm
Use the binomial distribution. The probabilities are described by
(1/3 + 2/3)^5
Find the term that as (1/3)^3 in it.
The binomial distribution is pretty easy to learn. You should read up on it in your book, in Wikipedia, or at Khan Academy. You need to learn it.
(1/3 + 2/3)^5
Find the term that as (1/3)^3 in it.
The binomial distribution is pretty easy to learn. You should read up on it in your book, in Wikipedia, or at Khan Academy. You need to learn it.
2016-08-01 11:35 pm
Hint:
X~Bi(n=5 , p =2/3)
X~Bi(n=5 , p =2/3)
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