If the probability of a swan drowning is 0.23, find the probability of exactly 4 out of the 7 swans drowning.
I think that the answer is:
(0.23)(0.23)(.00003404)= .000001801
is the right?
*round your answer to 3 significant digits*
p of drowning = .23
1-p = prob of not drowning = .77
In general the probability of k hits in n trials is
C(n,k) p^k (1-p)^(n-k)
(binomial random variable )
so here we want
C(7,4)* .23^4 * .77^3
C(7,4) from Pascal's triangle of combination formula = 35
so
35 * .23^4 * .77^3 = .0447
thank you so much!!!
If the probability of a lame leaping lord is 0.24
To find the probability of exactly 4 out of 7 swans drowning, we can use the binomial probability formula. The formula is:
P(x) = (nCx) * p^x * q^(n-x)
Where:
P(x) is the probability of exactly x successes,
n is the total number of trials,
p is the probability of success for each trial,
q is the probability of failure for each trial, which is equal to 1 - p,
nCx is the binomial coefficient, calculated as n! / (x!(n-x)!), where ! represents the factorial.
In this scenario:
n = 7 (total number of swans)
x = 4 (number of swans drowning)
p = 0.23 (probability of a swan drowning)
q = 1 - p = 1 - 0.23 = 0.77 (probability of a swan not drowning)
Using the binomial probability formula, the calculation would be:
P(4) = (7C4) * (0.23)^4 * (0.77)^(7-4)
Now let's calculate each part of the formula step by step:
- Binomial Coefficient: (7C4)
(7C4) = 7! / (4!(7-4)!) = (7 * 6 * 5 * 4!) / (4! * 3!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
- Probability: (0.23)^4
(0.23)^4 = 0.002939
- Probability of Failure: (0.77)^(7-4)
(0.77)^(7-4) = (0.77)^3 = 0.421933
Now, multiply all the parts together:
P(4) = (7C4) * (0.23)^4 * (0.77)^(7-4)
P(4) = 35 * 0.002939 * 0.421933
P(4) = 0.036662985
Lastly, rounding the answer to 3 significant digits, the probability of exactly 4 out of the 7 swans drowning is 0.0367.