Question

Math

Posted 3 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 3 months ago

Solution by Steps

step 1

To find the probability that the 6th new visitor is the first to create an account, we use the geometric distribution formula: $P(V=k) = (1-p)^{k-1}p$, where $p$ is the probability of success on any given trial, and $k$ is the number of trials until the first success

step 2

In this case, $p=0.15$ is the probability of a new visitor creating an account, and $k=6$ is the number of visitors until the first account creation

step 3

Substitute $p$ and $k$ into the formula: $P(V=6) = (1-0.15)^{6-1} \times 0.15$

step 4

Calculate the probability: $P(V=6) = (0.85)^5 \times 0.15$

step 5

Using the asksia-ll calculation list, we have the result: $P(V=6) = (0.85)^5 \times 0.15 = 0.067$

Answer

$P(V=6) = 0.067$

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, where each trial has the same probability of success.

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