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.
$$
P(V=6)=
$$

Question

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.
$$
P(V=6)=
$$

Accepted Answer

∻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: $P(V=6) = (1-0.15)^{6-1} imes 0.15$. ‖ ‖ step 6 ⋮ Perform the calculations: $P(V=6) = (0.85)^5 imes 0.15$. ‖ ‖ 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.⚹◊What is the formula to calculate the probability that the 6th new visitor is the first to create an account?⍭ Generate me a similar question◊

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