Answer:
The percent probability of winning a prize=40%.
and not winning prize=60%.
We are asked to find the probability that Hannah only has to buy 3 or less boxes before getting a prize.
Let the random used is x=0,1,2,3 ( where
- 0 denotes that we got the success in first attempt.
- 1 denotes that first bag does not contain prize but we get success in second attempt.
- 2 denotes that we did not get success in 2 attempts but in third we get the success.
- 3 denotes that the success is not obtained in any of the three attempts )
Hence, the probability that the first box will contain prize=[tex]\dfrac{40}{100}[/tex]
The probability that the first box will not contain prize but second will=[tex]\dfrac{60}{100}\times\dfrac{40}{100}[/tex]
The probability that the first and second box will not contain prize but third will=[tex]\dfrac{60}{100}\times\dfrac{60}{100}\times\dfrac{40}{100}[/tex]
The probability that the first and second box will not contain prize but third will=[tex]\dfrac{60}{100}\times\dfrac{60}{100}\times\dfrac{40}{100}[/tex]
The probability that the prize is not contained in first, second and third box=[tex]\dfrac{60}{100}+\times\dfrac{60}{100}\times\dfrac{60}{100}[/tex]
Hence, the total probability=
[tex]\dfrac{40}{100}+\dfrac{60}{100}\times\dfrac{40}{100}+\dfrac{60}{100}\times\dfrac{60}{100}\times\dfrac{40}{100}+\dfrac{60}{100}+\times\dfrac{60}{100}\times\dfrac{60}{100}[/tex]
