Sub-topic 1
2025 · National One-Eighth
Free
Probability that two fair dice give a total of $8$ with both scores even or both odd
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Sub-topic 2
2025 · National One-Eighth
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Probability that two fair dice give a total of $6$ with both scores odd (speed race)
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Sub-topic 4
2026 · National Preliminary
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Finding $x$ for independent events with $p(a)=x$, $p(b)=3x$ and $p(a\cap b)=\dfrac{1}{6}$
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Sub-topic 5
2026 · National Preliminary
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Finding $p(a)$ given $p(a\cup b)=\dfrac{4}{5}$, $p(a\cap b)=\dfrac{1}{3}$ and $p(b)=\dfrac{3}{5}$
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Sub-topic 6
2026 · National Preliminary
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Probability of exactly one head in three tosses of a coin with $p(h)=\dfrac{3}{5}$
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Sub-topic 7
2026 · National Preliminary
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Probability that an arrangement of $1,2,3,4,5$ begins and ends with an odd number
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Sub-topic 8
2026 · National Preliminary
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Probability of exactly one girl when $2$ students are chosen from $3$ boys and $2$ girls
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Sub-topic 9
2026 · National Preliminary
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$p(a\cup b)$ for independent events with $p(a)=\dfrac{1}{2}$ and $p(b)=\dfrac{1}{3}$
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Sub-topic 9
2026 · National Preliminary
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$p(a\cup b)$ for independent events with $p(a)=\dfrac{1}{2}$ and $p(b)=\dfrac{1}{3}$ (second contest)
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Sub-topic 10
2025 · National Preliminary
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Probability of no heads in $3$ tosses of a fair coin
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Sub-topic 11
2026 · National Quarterfinal
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Committee of three men and two women from four men and three women
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Sub-topic 12
2026 · National Quarterfinal
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Probability that the four consonants of the letters $a,b,c,d,e,f$ stay together
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Sub-topic 15
2026 · National One-Eighth
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Probability of exactly one head in three tosses of a coin with $p(h)=\dfrac{5}{8}$
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Sub-topic 16
2026 · National One-Eighth
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Committee of three men and two women from four men and three women (second contest)
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Sub-topic 17
2023 · National One-Eighth
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Selecting three students from three boys and four girls: gender compositions
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Sub-topic 18
2021 · National Preliminary
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Finding $x$ for disjoint events with $p(a)=x$, $p(b)=2x$ and $p(a\cup b)=\dfrac{3}{4}$
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Sub-topic 19
2026 · National Preliminary
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One girl and one boy chosen from three boys and two girls
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Sub-topic 19
2026 · National Preliminary
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One girl and one boy chosen from three boys and two girls (second contest)
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Sub-topic 20
2024 · National One-Eighth
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Committee of three chosen from five girls and three boys
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Sub-topic 21
2024 · National One-Eighth
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Riddle: independent events
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Sub-topic 22
2024 · National One-Eighth
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Finding $x$ for independent events with $p(a)=x$, $p(b)=2x$ and $p(a\cap b)=\dfrac{3}{8}$
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Sub-topic 23
2025 · National Final
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One white and one red ball drawn from $5$ white, $7$ black and $8$ red balls
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Sub-topic 23
2023 · National Preliminary
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Two white balls drawn without replacement from $6$ black and $4$ white balls
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Sub-topic 24
2023 · National Preliminary
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Arranging the letters of $party$: consonant first and vowel last
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Sub-topic 25
2013 · National Preliminary
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Probability of an even number from $s=\{1,2,\dots,9\}$
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Sub-topic 26
2013 · National Preliminary
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Probability of a prime number from $s=\{1,2,\dots,9\}$
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Sub-topic 27
2013 · National Preliminary
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Probability of an odd number greater than $4$ from $s=\{1,2,\dots,9\}$
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Sub-topic 28
2013 · National Quarterfinal
Premium
Finding $p(a\cup b)$ from $p(a)=0.6$, $p(b)=0.4$ and $p(a\cap b)=0.3$
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Sub-topic 29
2013 · National Quarterfinal
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Finding $p(a\cap b)$ from $p(a)=0.5$, $p(b)=0.6$ and $p(a\cup b)=0.8$
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Sub-topic 30
2013 · National Quarterfinal
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Finding $p(a)$ from $p(a\cup b)=0.6$, $p(a\cap b)=0.1$ and $p(b)=0.3$
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Sub-topic 31
2013 · National Semifinal
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Two girls given at least one girl among two children
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Sub-topic 32
2013 · National Semifinal
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Two girls given that the older child is a girl
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Sub-topic 33
2019 · National Preliminary
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A multiple of $2$ or a multiple of $3$ on a fair die
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Sub-topic 34
2023 · National Preliminary
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Committees of three chosen from four boys and six girls
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Sub-topic 35
2026 · National Semifinal
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Finding $p(a)$ and $p(b)$ for independent events with $p(a)=2x$, $p(b)=3x$ and $p(a\cap b)=\dfrac{1}{6}$
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Sub-topic 36
2025 · National Preliminary
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$p(a\cup b)$ for mutually exclusive events with $p(a)=\dfrac{2}{5}$ and $p(b)=\dfrac{3}{7}$
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Sub-topic 37
2025 · National Preliminary
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$p(a\cup b)$ from $p(a)=\dfrac{3}{5}$, $p(b)=\dfrac{2}{5}$ and $p(a\cap b)=\dfrac{1}{3}$
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