CulturalSinger
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In a binomial trail, the probability of success is 0.6 for each trial. Find the probability of each of the following.
51. 9 success in 20 trials
53. 6 failures in 12 trials
And could you show your work plz

Respuesta :

CastleRook
Binomial distribution is given by the formula:
p(x=r)=(n!/(r!(n-r)!))p^r q^(n-r)
thus:
a] Probability of obtaining 9 success in 20 trials will be:
P(x)=[20!/(9!(20-9)!)]*0.6^9*0.4^(20-9)
Simplifying the above we get:
P(x)=167960*0.6^9*0.4^11
P(x)=0.071

b] Probability of obtaining 6 failures in 12 trials
P(x)=[12!/(6!(12-6)!)]*0.4^6*(0.6)^(12-6)
simplifying the above we obtain:
P(x)=924*0.4^6*0.6^6
P(x)=0.1766

Answer with Step-by-step explanation:

The formula for finding the probability of r success in binomial trail is:

P(r success) =  [tex]\dfrac{n!}{(n-r)!r!}p^rq^{n-r}[/tex]

where n is the number of trials,p is the probability of success and q is the probability of failure.

q=1-p

Here, p=0.6

⇒q=1-0.6

⇒q=0.4

9 success in 20 trials

r=9 and n=20

P(9 success)= [tex]\dfrac{20!}{(20-9)!9!}0.6^90.4^{20-9}[/tex]

                   =  [tex]\dfrac{20!}{11!9!}0.6^90.4^{11}[/tex]

                  = 0.07

6 failures in 12 trials

P(6 failures)=P(12-6 success)

                  =P(6 success)

                 =  [tex]\dfrac{12!}{(12-6)!6!}0.6^60.4^{12-6}[/tex]

                =  [tex]\dfrac{12!}{6!6!}0.6^60.4^6[/tex]

                = 0.18

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