Consider a binominal experiment with 2 trials and $p=0.4$

a. Compute the probability of 1 success f(1)

b. Compute f(0)

c. Compute f(2)

a. Compute the probability of 1 success f(1)

b. Compute f(0)

c. Compute f(2)

sanuluy
2021-09-28
Answered

Consider a binominal experiment with 2 trials and $p=0.4$

a. Compute the probability of 1 success f(1)

b. Compute f(0)

c. Compute f(2)

a. Compute the probability of 1 success f(1)

b. Compute f(0)

c. Compute f(2)

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Alix Ortiz

Answered 2021-09-29
Author has **109** answers

Step 1

Given binomial experiment with$n=2\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}p=0.4$

The binomial probability for x number of success is calculated by the below mentioned formula

$P(X=x){=}^{n}{C}_{x}{\left(p\right)}^{x}{(1-p)}^{n-x}$

Step 2

The probability of 1 success is computed as shown below

Probability of 1 success$f\left(1\right)=0.48$

$P(X=x){=}^{n}{C}_{x}{\left(p\right)}^{x}{(1-p)}^{n-x}$

$P(X=1){=}^{2}{C}_{1}{\left(0.4\right)}^{1}{(1-0.4)}^{2-1}$

$P(X=1)=2\cdot \left(0.4\right)\cdot \left(0.6\right)=0.48$

Step 3

The probability of 0 success is computed as shown below

The probability of 0 success is$f\left(0\right)=0.36$

$P(X=x){=}^{n}{C}_{x}{\left(p\right)}^{x}{(1-p)}^{n-x}$

$P(X=0){=}^{2}{C}_{0}{\left(0.4\right)}^{0}{(1-0.4)}^{2-0}$

$P(X=0)=1\cdot \left(1\right)\cdot {\left(0.6\right)}^{2}=0.36$

Step 4

The probability of 2 success is computed as shown below

The probability of 2 success$f\left(2\right)=0.16$

$P(X=x){=}^{n}{C}_{x}{\left(p\right)}^{x}{(1-p)}^{n-x}$

$P(X=2){=}^{2}{C}_{2}{\left(0.4\right)}^{2}{(1-0.4)}^{2-2}$

$P(X=2)=1\cdot {\left(0.4\right)}^{2}\cdot {\left(0.6\right)}^{0}=0.16$

Given binomial experiment with

The binomial probability for x number of success is calculated by the below mentioned formula

Step 2

The probability of 1 success is computed as shown below

Probability of 1 success

Step 3

The probability of 0 success is computed as shown below

The probability of 0 success is

Step 4

The probability of 2 success is computed as shown below

The probability of 2 success

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