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Lesson: Binomial Experiments

Worksheet • 3 Questions

Q1:

Follow the steps to construct a binomial experiment to find the experimental probability of rolling two dice and obtaining two numbers which sum to more than 10.

One trial of the experiment would be rolling two dice and we will conduct 25 trials. How would we define success for each trial?

  • AGetting two numbers which sum to 10
  • BGetting two numbers which sum to more than 10
  • CGetting two numbers which sum to less than 10

State the probability, 𝑝 , of a success as a fraction in its simplest form.

  • A 1 1 2
  • B 1 3 6
  • C 1 6
  • D 1 2
  • E 1 3

State the probability of a failure.

  • A 1 1 1 2
  • B 2 3
  • C 5 6
  • D 1 2
  • E 3 5 3 6

Describe the random variable 𝑋 in this experiment, which is binomially distributed.

  • A 𝑋 is the number of times we get two numbers which sum to 10 in our 25 trials.
  • B 𝑋 is the number of times we get two numbers which sum to more than 10 in our 25 trials.
  • C 𝑋 is the number of times we get two numbers which sum to less than 10 in our 25 trials.

Q2:

Decide if the following experiment is a binomial experiment: drawing cards from a deck of 52 cards to see how many times the number 5 appears.

If it is, state the probability of a success as a fraction.

  • ANot a binomial experiment
  • BA binomial experiment, with 𝑝 = 1 1 3

Q3:

In a binomial experiment, this spinner is spun 10 times and we record the number of times that the top score is achieved.

Let 𝑋 be the number of successes.

Determine 𝑃 ( 𝑋 = 2 ) as a percentage to 3 decimal places.

  • A 2 8 . 1 5 7 %
  • B 1 8 . 7 7 1 %
  • C 1 4 . 5 9 9 %
  • D 2 5 . 0 2 8 %
  • E 0 . 6 1 7 %

Determine 𝑃 ( 𝑋 = 9 ) as a percentage to 3 decimal places.

  • A 0 . 0 0 3 %
  • B 2 8 . 1 5 7 %
  • C 0 . 0 0 5 %
  • D 1 . 6 2 2 %
  • E 0 . 0 0 8 %
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