Mathematics, 04.04.2021 06:00 musa79

find the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any trial is 9%

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Answer from: yasameenakbari

0.8746 = 87.46% probability of at least 6 failures in 7 trials.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

7 trials

This means that n = 7

The probability of success in any trial is 9%?

So the probability of a failure is 100 - 9 = 91%, which means that p = 0.91

Probability of at least 6 failures in 7 trials?

This is:

$P(X \geq 6) = P(X = 6) + P(X = 7)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 6) = C_{7,6}.(0.91)^{6}.(0.09)^{1} = 0.3578$

$P(X = 7) = C_{7,7}.(0.91)^{7}.(0.09)^{0} = 0.5168$

$P(X \geq 6) = P(X = 6) + P(X = 7) = 0.3578 + 0.5168 = 0.8746$

0.8746 = 87.46% probability of at least 6 failures in 7 trials.

Answer from: Quest

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Answer from: Quest

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

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