Calculating Binomial Probabilities

	Calculating Binomial Probabilities It is important to understand and be able to apply the formula for calculating Binomial probabilities. However, once you have mastered the technique, it is not sensible to use hand calculation to solve routine problems. In this section we provide you with a spreadsheet which calculates Binomial probabilities for you. You can either use it to replace hand calculation or as a way of checking your answers to problems solved by hand. For large values of n the results of the spreadsheet may become unreliable.
	Just click on the link below to load the Excel Calculator spreadsheet. When you have finished, use the browser's Back button to return here. Load spreadsheet
	Example To see how the Binomial formula works in practice, consider the example of biros sold in packets of 10, where 5% of biros are defective on average. Suppose that a packet is selected at random. Taking n=10 and p=0.05: Pr ( 0 defectives in packet) = ¹⁰C₀ 0.05⁰ 0.95¹⁰ = 1 x 1 x 0.5987 = 0.5987 Pr ( 1 defective in packet) = ¹⁰C₁ 0.05¹ 0.95⁹ = 10 x 0.05 x 0.6302 = 0.3151 Pr ( 2 defectives in packet) = ¹⁰C₂ 0.05² 0.95⁸ = 45 x 0.0025 x 0.6634 = 0.0746 Pr ( 3 defectives in packet) = ¹⁰C₃ 0.05³ 0.95⁷ = 120 x 0.000125 x 0.6983 = 0.0105 etc. Pr ( less than 3 defectives in packet) = Pr(0) + Pr(1) + Pr(2) = 0.5987 + 0.3151 + 0.0746 = 0.9884 Pr ( at least 3 defectives in packet) = Pr(3) + Pr(4) + Pr(5) + ... = 1 - { Pr(0) + Pr(1) + Pr(2) } = 1 - 0.9884 = 0.0116 Use the Calculator spreadsheet to check these answers using Excel's functions. The Calculator spreadsheet allows you to calculate Binomial probabilities for any values of n and p. If you are using hand calculation, for large values of n it is more convenient to use a Normal approximation to calculate Binomial probabilities.
	To continue on the recommended route click on the Normal button at the top of the page.

Calculating Binomial Probabilities

Example