State general binomial conditions

Questions that ask students to state or list the general conditions required for a binomial distribution without reference to a specific context.

5 questions · Moderate -0.8

2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities
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CAIE S1 2014 June Q3
5 marks Moderate -0.8
3
  1. State three conditions which must be satisfied for a situation to be modelled by a binomial distribution. George wants to invest some of his monthly salary. He invests a certain amount of this every month for 18 months. For each month there is a probability of 0.25 that he will buy shares in a large company, there is a probability of 0.15 that he will buy shares in a small company and there is a probability of 0.6 that he will invest in a savings account.
  2. Find the probability that George will buy shares in a small company in at least 3 of these 18 months.
CAIE S1 2004 November Q7
10 marks Moderate -0.8
7
  1. State two conditions which must be satisfied for a situation to be modelled by a binomial distribution. In a certain village 28\% of all cars are made by Ford.
  2. 14 cars are chosen randomly in this village. Find the probability that fewer than 4 of these cars are made by Ford.
  3. A random sample of 50 cars in the village is taken. Estimate, using a normal approximation, the probability that more than 18 cars are made by Ford.
CAIE S1 2010 November Q6
10 marks Moderate -0.8
6
  1. State three conditions that must be satisfied for a situation to be modelled by a binomial distribution. On any day, there is a probability of 0.3 that Julie's train is late.
  2. Nine days are chosen at random. Find the probability that Julie's train is late on more than 7 days or fewer than 2 days.
  3. 90 days are chosen at random. Find the probability that Julie's train is late on more than 35 days or fewer than 27 days.
OCR S1 2005 January Q7
9 marks Easy -1.2
7 It is known that, on average, one match box in 10 contains fewer than 42 matches. Eight boxes are selected, and the number of boxes that contain fewer than 42 matches is denoted by \(Y\).
  1. State two conditions needed to model \(Y\) by a binomial distribution. Assume now that a binomial model is valid.
  2. Find
    1. \(\mathrm { P } ( Y = 0 )\),
    2. \(\mathrm { P } ( Y \geqslant 2 )\).
    3. On Wednesday 8 boxes are selected, and on Thursday another 8 boxes are selected. Find the probability that on one of these days the number of boxes containing fewer than 42 matches is 0 , and that on the other day the number is 2 or more.
Edexcel S2 2003 June Q4
12 marks Moderate -0.3
  1. Write down the conditions under which the binomial distribution may be a suitable model to use in statistical work. [4]
A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly. Find the probability that
    1. the first 5 will occur on the sixth throw,
    2. in the first eight throws there will be exactly three 5s.
    [8]