Mipango

Kikokotoo cha Uwezekano

Kokotoa uwezekano kutoka matokeo yanayotakiwa na matokeo yote, au unganisha matukio mawili huru (A na B, A au B, hakuna kati yao, moja tu).

Matokeo unayotaka, k.m. mipira 3 myekundu
Matokeo yote yenye uwezekano sawa

Tokeo

Weka thamani kisha bonyeza Kokotoa ili kuona tokeo.

Fomula

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.

Jinsi ya kutumia kikokotoo hiki

  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).

Mfano uliotatuliwa

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).

Maswali yanayoulizwa mara kwa mara

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).