Binomial distribution

Lessons

• Introduction
  a)

  Binomial
  
  
  b)

  Binomial Formula
  
  
  c)

  Binomialpdf Calculator
  
  

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• 1.
  Identify which of the following experiments below are binomial distributions?
  
  i. A fair die is rolled 4 times. What is the probability of the one coming up 2 times?
  
  ii. A fair coin is flipped until head comes up 7 times. What is the probability that the coin will be flipped 10 times?
  
  iii. 1,000,000 nails are produced in a factory a day. If each nail has a probability of 0.5% of being defective (something being wrong with that nail), then what is the probability that less than 50 nails will be defective in a day?
  
  iv. Roughly 7.5% of Canadians have some form of heart disease. If 100 Canadians are sampled what is the probability that 10 of them will have heart disease?
  
  v. If 5 cards are drawn from a deck, what is the probability that 2 of them will be hearts?
  
  vi. If a fair die is rolled 8 times, what is the probability of getting 2 fours and 3 sixes?
  

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• 2.
  An urn contains 6 red balls and 4 green balls. A total of 5 balls are drawn; list all the different combinations of red balls that can be drawn in each of the following cases:
  
  i. A total of 3 green balls are drawn
  
  ii. At most 3 red balls are drawn
  
  iii. At least 2 red balls are drawn
  
  iv. Less than 4 red balls are drawn
  
  v. More than 3 green balls are drawn
  

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• 3.
  A die is rolled 3 times, what is the probability that a four is rolled exactly 2 times?

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• 4.
  A coin is flipped 20 times, what is the probability that the coin comes up heads 15 times?

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• 5.
  Jimmy the Joker is an unfair gambler. He weights a die so it rolls a "6" with 75% chance. He then bets that if he rolls his die 4 times he will roll six exactly 3 times. What is his probability of winning this bet?

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• 6.
  Thomas is packing for a trip and wants to bring some stuffed animals along for comfort. He owns 8 stuffed animals, and will pack each stuffed animals independently of all the others with a probability of 30%. Determine the probability that he takes;
  
  a)

  0 stuffed animals along with him.
  
  
  b)

  1 stuffed animal with him
  
  
  c)

  at most two animals along with him.
  
  
  d)

  at most 5 animals along with him.
  
  
  e)

  at least 6 animals along with him.
  
  

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