Probability problems

Every probability question uses the same routine:

• count all the possible outcomes
• count the favourable ones (the ones the question asks about)
• divide, and check that the outcomes really are equally likely

A piggy bank holds 100 fifty-paise coins, 50 ₹1 coins, 20 ₹2 coins and 10 ₹5 coins: 180 in all. P(not a ₹5 coin) = 170/180 = 17/18.

Taking things out without putting them back changes the totals. A box has 20 bulbs, 4 of them faulty. One good bulb is taken out and not replaced. Now 19 are left, and 15 of them are good, so P(the next is good) = 15/19.

Numbers on cards or discs: list them. Discs 1 to 90: the perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81. That's 9, so P = 9/90 = 1/10.

From a probability back to a number: if P(a blue marble) = 2/3 with 12 marbles in all, then 2/3 × 12 = 8 are blue.

Is it equally likely? Think before you use the formula.

• A coin toss to decide which team starts is fair: heads and tails are equally likely.
• 'Will the car start or not?' is not a 50–50 question: a car usually starts.
• Odd or even on a fair die is equally likely: 3 faces each.