Calculating Binomial Probability using Combinations

00:00 3 marks

  • Exam Style - Paper 2
  • SL & HL
  • Tier 2
  • Binomial distribution
  • Probability
  • Combinations
  • nCk

A factory produces light bulbs, and it is known that 10% of the bulbs are defective. In a random sample of 10 bulbs, calculate the probability that exactly 3 bulbs are defective. Use combination logic and show your working.

Hint Hint

Hint

Recall the binomial probability formula: \(P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}\). Identify \(n\) as the sample size, \(k\) as the number of defective bulbs (successes), and \(p\) as the probability of a bulb being defective.

  • Answer Answer
  • Mark Scheme Mark Scheme
  • Explanation Explanation
  • Examiner Tips Examiner Tips
  • Common Errors Common Errors
  • Real World Context Real World Context
  • Focus Focus
  • Formula Booklet
  • Answer Answer

Complete Answer

0.0574

  • Mark Scheme Mark Scheme
  • Answer Explanation Answer Explanation
  • Examiner Tips Examiner Tips
  • Common Errors Common Errors
  • Focus Focus

Math Editor

Report Question


Please enter keywords