A website offers a coupon such that each customer has a $15 \%$ chance of getting the coupon each day they visit the site. Aya visits the website for 6 consecutive days.

What is the probability that Aya will be offered a coupon on at least one of the days she visits the website?
Round your answer to the nearest hundredth.
$P($ at least one coupon $)=$ $\square$

Question

A website offers a coupon such that each customer has a $15 \%$ chance of getting the coupon each day they visit the site. Aya visits the website for 6 consecutive days.

What is the probability that Aya will be offered a coupon on at least one of the days she visits the website?
Round your answer to the nearest hundredth.
$P($ at least one coupon $)=$ $\square$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the probability that Aya does not get a coupon on a single day, which is $1 - 0.15 = 0.85$. ‖ ‖ step 2 ⋮ Calculate the probability that Aya does not get a coupon on any of the 6 days she visits, which is $(0.85)^6$. ‖ ‖ step 3 ⋮ Use the asksia-ll calculator result for $(0.85)^6$, which is $1 - (1 - 0.15)^6 = 0.62285$. ‖ ‖ step 4 ⋮ Subtract this probability from 1 to find the probability that Aya gets a coupon on at least one day, which is $1 - 0.62285$. ‖ ‖ step 5 ⋮ Calculate the final probability, which is $1 - 0.62285 = 0.37715$. ‖ ‖ step 6 ⋮ Round the final probability to the nearest hundredth, which is $0.38$. ‖ ∻[1] Answer∻ ⚹ $P($ at least one coupon $) = 0.38$ ⚹ ∻Key Concept∻ ⚹Complementary Probability⚹ ∻Explanation∻ ⚹The probability of Aya receiving at least one coupon is found by subtracting the probability of her not receiving a coupon on any day from 1. This is known as the complementary probability.⚹◊What is the formula for calculating the probability of at least one event occurring in a series of independent events?⍭ Generate me a similar question◊

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