Simulation · Maths · Class 11

Load the six and watch every face

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

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.

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