プラン

確率の計算機

起こってほしい場合の数と全体の場合の数から確率を求めたり、2 つの独立な事象（A かつ B、A または B、どちらも起こらない、ちょうど 1 つ）を組み合わせたりします。

求めたい結果、例：赤い玉 3 個
同様に確からしいすべての結果

結果

値を入力して「計算」を押すと結果が表示されます。

公式

P(E)=favourable outcomestotal outcomesP(E) = \frac{\text{favourable outcomes}}{\text{total outcomes}}

For equally likely outcomes.

P(not E)=1−P(E)P(\text{not } E) = 1 - P(E)

The complement: the event does not happen.

P(A∩B)=P(A) P(B)P(A \cap B) = P(A)\,P(B)

Both happen, when A and B are independent.

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)

At least one happens.

この計算ツールの使い方

  1. For one event, enter how many outcomes you want and how many there are in total.
  2. For two independent events, enter each probability as a fraction (1/2) or a decimal (0.5).

解き方付き例題

3 red balls in a bag of 8

P(red) = 3/8 = 0.375 = 37.5%.

P(not red) = 1 − 3/8 = 5/8.

The odds of red are 3 : 5 (3 for, 5 against).

よくある質問

What does independent mean?

One event does not change the chance of the other — like two separate coin flips.

What is the difference between probability and odds?

Probability compares favourable outcomes with all outcomes (3/8); odds compare favourable with unfavourable (3 : 5).