Respuesta :
Answer:
[tex]P(X \geq 2)= 1-P(X<2) = 1-P(X\leq 1) = 1-P(X =1)[/tex]
And if we replace we got:
[tex]P(X \geq 2)= 1-P(X<2) = 1-P(X\leq 1) = 1-[(1-381)^{1-1}*0.381]= 1-0.381 = 0.619[/tex]
Step-by-step explanation:
Previous concepts
The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"
[tex]P(X=x)=(1-p)^{x-1} p , x= 1,2,3,...[/tex]
Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:
[tex]X\sim Geo (1-p)[/tex]
Solution to the problem
For this case the totla number of bulbas are: 7+6+8= 21
For this case we have eight 75W
And we can find the probability of success on this case like this:
[tex] p = \frac{8}{21}=0.381[/tex]
And let X the random variable that represent the number of 75-W bulbs, then we have that [tex] X \sim Geo (1-0.381)[/tex]
And we want to find this probability:
[tex] P(X \geq 2)[/tex]
We can use the complement rule and we have:
[tex]P(X \geq 2)= 1-P(X<2) = 1-P(X\leq 1) = 1-P(X =1)[/tex]
And if we replace we got:
[tex]P(X \geq 2)= 1-P(X<2) = 1-P(X\leq 1) = 1-[(1-381)^{1-1}*0.381]= 1-0.381 = 0.619[/tex]
