Question

Math

Posted 4 months ago

```
New visitors to a certain website have a 0.15 probability of creating an account on their first visit. Let $V$ be the number of new visitors who visit the site until the first one of them creates an account. Assume that each visitor's decision to create an account or not is independent.
Find the probability that the $6^{\text {th }}$ new visitor is the first to create an account.
You may round your answer to the nearest hundredth.
$P(V=6)=$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Identify the type of distribution that applies to the problem

step 2

Recognize that the problem follows a geometric distribution since we are looking for the probability of the first success on the 6th trial

step 3

Use the formula for the geometric distribution: $P(V=k) = (1-p)^{k-1}p$, where $p$ is the probability of success on any given trial, and $k$ is the trial number of the first success

step 4

Substitute $p = 0.15$ and $k = 6$ into the formula

step 5

Calculate the probability: $P(V=6) = (1-0.15)^{6-1} \times 0.15$

step 6

Perform the calculations: $P(V=6) = (0.85)^5 \times 0.15$

step 7

Round the result to the nearest hundredth

Answer

$P(V=6) \approx 0.05$

Key Concept

Geometric Distribution

Explanation

The geometric distribution is used to model the number of trials until the first success in a series of independent Bernoulli trials.

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