Answer :
Answer:
(a) [tex]\approx[/tex] 0.32
(b) [tex]\approx[/tex] 0.68
Step-by-step explanation:
It is given that a binomial experiment is carried out.
n = 4 trials
Probability of success, p = 0.25
We know that in a binomial experiment:
Probability of success + Probability of failure = 1
p + q = 1
So, q = 1 - 0.25 = 0.75
Probability of 'r' number of successes in 'n' trials of a binomial experiment is given as:
[tex]P(r=x) = _nC_x\times p^x(q)^{n-x}[/tex]
(a) P(r = 0) = ?
Putting values of x = 0, p and q:
[tex]P(r=0) = _4C_0\times (0.25)^0\times (0.75)^{4-0}\\P(r=0) = 1\times 1\times (0.75)^{4}\\P(r=0) \approx 0.32[/tex]
(b) Find P(r ≥ 1) = ?
Using complement rule:
P(r =0 ) + P(r ≥ 1) = 1
0.32 + P(r ≥ 1) = 1
P(r ≥ 1) = 1 - 0.32
P(r ≥ 1) = 0.68
So, the answer are:
(a) [tex]\approx[/tex] 0.32
(b) [tex]\approx[/tex] 0.68
In binomial experiment with 4 trials, Probabilities shown below.
[tex]P(r=0)=0.32[/tex] and [tex]P(r\geq 1)=0.68[/tex]
The Probability of r number of successes in n trials is given by a binomial expression,
[tex]P(X=r)=^{n}C_{r}q^{n-r}p^{r}[/tex]
Where p represent probability of success and q represent probability of unsuccessful.
Number of trials, n = 4
Probability of success, p = 0.25 and q = 1 - 0.25 = 0.75
[tex]P(r=0)=^{4}C_{0}(0.75)^{4}(0.25)^{0}=1*(0.75)^{4}*1=0.32[/tex]
[tex]P(r\geq 1)=1-P(r=0)\\\\P(r\geq 1)=1-0.32=0.68[/tex]
Learn more about binomial expression here :
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