Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
The probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.
What is Binomial distribution?
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given that a box of trading cards contains 24-packs of cards in it. And Only two of those packs contain limited edition cards. Therefore, the probability of finding a limited edition card will be,
[tex]P = \dfrac2{24} = \dfrac{1}{12}[/tex]
The probability of not getting a limited edition card will be,
[tex]q = \dfrac{24-2}{24} = \dfrac{22}{24} = \dfrac{11}{12}[/tex]
Now, using the binomial distribution, the probability can be found.
A.) The probability that a collector will find both limited edition cards if he buys only 2 packs is
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=2) = ^2C_2 \cdot(\dfrac1{12})^2 \cdot (\dfrac{11}{12})^{(0)}\\\\P(x = 2) = 0.0069 \approx 0.007[/tex]
B.) The probability that he gets at least one limited edition card if he buys 3 packs can be written as,
The probability of at least a limited edition card
= 1 - Probability of not getting any limited edition card
The probability of getting no special edition card will be,
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=0) = ^3C_0 \cdot(\dfrac1{12})^0 \cdot (\dfrac{11}{12})^{(3)}\\\\P(x = 0) = 0.77[/tex]
Now,
The probability of at least a limited edition card
= 1 - Probability of not getting any limited edition card
The probability of at least a limited edition card = 1 - P(x=0) = 1-0.77 = 0.23
Hence, the probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.
Learn more about Binomial Distribution:
https://brainly.com/question/14565246
#SPJ1
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
