Multiple choice

Piggybank contains $100$ fifty-paise coins, $50$ one-rupee coins, $20$ two-rupees coins and $10$ five- rupees coins. One coin is drawn at random. Find the probability that the drawn coin (i) will be a fifty-paise coin (ii) will not be a five-rupees coin.

  1. (i) $\dfrac{4}{9}$    (ii) $\dfrac{17}{18}$ 
  2. (i) $\dfrac{5}{9}$    (ii) $\dfrac{17}{18}$ 
  3. (i) $\dfrac{5}{9}$    (ii) $\dfrac{14}{18}$ 

  4. None of these
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B Correct answer
Explanation

Total coins = 100 + 50 + 20 + 10 = 180. (i) P(fifty-paise) = 100/180 = 5/9. (ii) P(not five-rupees) = 1 - P(five-rupees) = 1 - 10/180 = 1 - 1/18 = 17/18.

AI explanation

The total number of coins in the piggybank is 100 + 50 + 20 + 10 = 180. For the first part, the probability of drawing a fifty-paise coin is the 100 fifty-paise coins divided by the total 180 coins, which simplifies to 5/9. For the second part, since there are 10 five-rupee coins, the probability of drawing a coin that is not a five-rupee coin is calculated by subtracting the probability of drawing one from 1, yielding 1 minus (10/180), which equals 170/180 or 17/18.

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