Understanding Probability Distribution in Baseball Card Packs

Hugo plans to buy baseball card packs until he finds his favorite player's card, with a maximum of four packs. Each pack has a 0.2 probability of containing the desired card. The video explains the probability distribution for the number of packs Hugo buys, denoted as random variable X. It calculates the probability of buying one, two, three, or four packs, emphasizing that the probabilities must sum to one. The video also explores the probability that X is greater than or equal to two, highlighting the high probability of buying four packs due to the stopping condition.

What is the maximum number of baseball card packs Hugo can buy?

• Five

• Four

• Three

• Two

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What is the probability that Hugo buys exactly one pack?

• 0.1

• 0.2

• 0.4

• 0.3

If Hugo doesn't get his favorite card in the first pack, what is the probability he gets it in the second pack?

• 0.18

• 0.16

• 0.22

• 0.2

What is the probability that Hugo buys exactly three packs?

• 0.148

• 0.158

• 0.138

• 0.128

How can we find the probability of Hugo buying four packs?

• By guessing

• By subtracting known probabilities from one

• By adding all probabilities

• By multiplying probabilities

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What is the probability that Hugo buys four packs?

• 0.712

• 0.612

• 0.512

• 0.412

Why is there a high probability that Hugo buys four packs?

• Because he has unlimited money

• Because he always gets the card in the fourth pack

• Because he buys packs in bulk

• Because he stops at four packs regardless

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What is the combined probability of Hugo buying two or more packs?

• 0.9

• 0.8

• 0.7

• 0.6

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What does the sum of all probabilities in a distribution equal?

• 2

• 1.5

• 1

• 0.5

What is the probability that Hugo gets his favorite card before buying four packs?

• 100%

• More than 50%

• Exactly 50%

• Less than 50%