Question

Math

Posted 6 months ago

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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 $)=$ $\square$
```

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Answer from Sia

Posted 6 months ago

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.

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