Question

37
In binomial probability distribution, if n=3 and p=0.5
then P(X=1) =
0.3
In binomis orohobi​

Answer 1

SOLUTION

GIVEN

In binomial probability distribution n = 3 and p = 0.5

TO DETERMINE

P(X=1)

CONCEPT TO BE IMPLEMENTED

If a trial is repeated n times and p is the probability of a success and q that of failure then the probability of r successes is

$\displaystyle \sf{ \sf{P(X=r) = \: \: }\large{ {}^{n} C_r}\: {p}^{r} \: \: {q}^{n - r} } \: \: \: \: \: where \: q \: = 1 - p$

EVALUATION

Here it is given that in a binomial probability distribution n = 3 and p = 0.5

We know that

$\displaystyle \sf{ \sf{P(X=r) = \: \: }\large{ {}^{n} C_r}\: {p}^{r} \: \: {q}^{n - r} } \: \: \: \: \: where \: q \: = 1 - p$

Now

$\displaystyle \sf{ \sf{P(X=1) = \: \: }\large{ {}^{3} C_1}\: {(0.5)}^{1} \: \: {(1 - 0.5)}^{3 - 1} }$

$\displaystyle \sf{ \implies P(X=1) = 3 \times \: {(0.5)}^{1} \times {( 0.5)}^{2} }$

$\displaystyle \sf{ \implies P(X=1) = 3 \times \: {(0.5)}^{3} }$

$\displaystyle \sf{ \implies P(X=1) = 3 \times \: 0.125 }$

$\displaystyle \sf{ \implies P(X=1) = 0.375 }$

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