Probability

Maths · Class 11

Simulation · Maths · Class 11

Load the six and watch every face

"Load the six and watch every face" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Probability of an event" in Probability. The mela's trick die (made up): face 6 is w times as likely as each other face. The six bars are the outcome probabilities, which always add to 1. Orange faces make up the chosen event, and P(event) is the sum of their bars. P(A) is the sum of the probabilities of the outcomes in A. The formula m/n works only when every outcome is equally likely.

From the lesson Probability of an event in Probability. Change the values and watch what happens.

Load the six and watch every faceMaths · Class 11

The idea behind it

NCERT §14.2.1

  • Once each outcome has its probability, P(A) is simply the sum of the probabilities of the outcomes inside A.
  • Three consecutive pens from a machine, each good (G) or defective (B): S = {BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG}. With 1/8 on each outcome, 'exactly one defective' = {BGG, GBG, GGB} has P = 3/8 and 'at least two defective' has P = 4/8 = 1/2.
  • Outcomes need not carry equal weight. For two tosses NCERT uses P(HH) = 1/4, P(HT) = 1/7, P(TH) = 2/7, P(TT) = 9/28, which add to 1.
  • Then 'both tosses give the same result' = {HH, TT} has P = 1/4 + 9/28 = 4/7, and 'exactly two heads' = {HH} has P = 1/4.
  • Mela trick die (made up): face 6 is weighted to be w times as likely as each other face. The weights add to w + 5, so P(6) = w/(w + 5) and every other face gets 1/(w + 5).
  • With w = 5: P(6) = 1/2 and each other face 1/10. So P(even) = 1/10 + 1/10 + 1/2 = 7/10, P(greater than 4) = 1/10 + 1/2 = 3/5 and P(prime) = 3/10. With w = 1 the die is fair and P(6) = 1/6.

Questions

2 answers

What does the "Load the six and watch every face" simulation show?
The mela's trick die (made up): face 6 is w times as likely as each other face. The six bars are the outcome probabilities, which always add to 1. Orange faces make up the chosen event, and P(event) is the sum of their bars.
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Probability of an event" in Probability (Class 11 Maths).

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