Question

7. At a fair, Evie gets five darts she can toss at balloons. If there is a probability of that any given dart she

Answer 1

Using the binomial distribution, it is found that the probability she will hit at least one balloon with her five darts is:

(1) 41%.

What is the binomial distribution formula?

The formula is:

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

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

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

In this problem, we have that:

• The probability of a single dart hitting is of p = 1/10 = 0.1.

• She will throw five darts, hence n = 5.

The probability of hitting at least one is given by:

$P(X \geq 1) = 1 - P(X = 0)$

In which:

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

$P(X = 0) = C_{5,0}.(0.1)^{0}.(0.9)^{5} = 0.59$

Then:

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.59 = 0.41$

Which means that option 1 is correct.

More can be learned about the binomial distribution at brainly.com/question/24863377

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