Probability of Remainder

Question

Ashok has a bag containing 40 cards, numbered with the integers from 1 to 40. No two cards are numbered with the same integer. Likewise, his sister Shilpa has another bag containing only five cards that are numbered with the integers from 1 to 5, with no integer repeating. Their mother, Latha, randomly draws one card each from Ashok’s and Shilpa’s bags and notes down their respective numbers. If Latha divides the number obtained from Ashok’s bag by the number obtained from Shilpa’s, what is the

Accepted Answer

E. Total outcomes = $40 	imes 5 = 200$. We want remainder $R \le 2$ when card $A \in [1, 40]$ is divided by $S \in [1, 5]$. - $S = 1$: Remainder is always 0 $\le 2$ (40 favorable). - $S = 2$: Remainder is 0 or 1 $\le 2$ (40 favorable). - $S = 3$: Remainder is 0, 1, or 2 $\le 2$ (40 favorable). - $S = 4$: Remainder can be 0, 1, 2, or 3. Remainder 3 occurs when $A \equiv 3 \pmod 4$. In $1..40$, 10 such numbers. Favorable = $40 - 10 = 30$. - $S = 5$: Remainder can be 0, 1, 2, 3, 4. Remainders 3 and 4 fail. Numbers $\equiv 3, 4 \pmod 5$ in $1..40$ are $8 + 8 = 16$. Favorable = $40 - 16 = 24$. Total favorable = $40 + 40 + 40 + 30 + 24 = 174$. Probability = $\frac{174}{200} = 0.87$.

Answer

0.8

Answer

0.91

Answer

0.73

Answer

0.94

Answer

0.87

Probability of Remainder

Explanation

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