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pacers vs thunder game 3 - Redraw

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Given the rectangle has sides 5 cm and 12 cm, the diagonal $ d $ is:

📌 $$Question: A climate resilience planner is analyzing temperature data over 7 consecutive days and notes that each days temperature anomaly (deviation from average) is an integer between $-3$ and $3$, inclusive. What is the probability that the sum of all 7 daily anomalies is exactly zero?

📌 We are given that each daily temperature anomaly is an integer from $-3$ to $3$, inclusive. There are $7$ independent days, and we want the probability that the sum of the 7 anomalies equals zero.

📌 We use generating functions. The generating function for one day is:

📌 So the number of favorable sequences is $60691$.

📌 This fraction is already in lowest terms (can be verified via GCD computation), so the final answer is:

📌 Question: A university professor assigns a genetics research project where students must simulate genetic drift using 6 alleles of varying frequencies. If each allele is modeled as being passed independently with probability proportional to its frequency, and each simulation run selects one allele uniformly based on relative frequency, what is the probability that in 10 consecutive simulations, exactly 3 distinct alleles appear?

📌 We are to compute the probability that in 10 independent trials (simulations), exactly 3 distinct alleles among 6 are observed, where at each step, an allele is selected with probability proportional to its frequency (i.e., multinomial sampling without replacement — but since no actual frequencies are given, assume uniform distribution over alleles for symmetry). However, the problem states selected uniformly based on relative frequency, but without specific weights, and to make it solvable, we interpret that each allele has equal chance — or more naturally, that the selection is uniform over the 6 alleles at each step (i.e., discrete uniform).

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