Question

В табуне 10 жеребцов, 15 кобыл, 20 жеребят. Вероятность быть заарканеным для жеребца = 0,2 , кобылы = 0,3 , жеребенка = 0,6. 1) С какой вероятность будет заарканена одна особь из табуна? 2) Арканом поймали лошадь. Найти вероятность того что это жеребец.

Answer 1

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Answer 2

Probability of an individual being branded in the herd

To calculate the probability of an individual being branded in the herd, we need to consider the probabilities for each type of horse (stallion, mare, and foal) being branded.

Given: - Number of stallions (жеребцов) = 10 - Number of mares (кобыл) = 15 - Number of foals (жеребят) = 20 - Probability of a stallion being branded = 0.2 - Probability of a mare being branded = 0.3 - Probability of a foal being branded = 0.6

1) Probability of one individual being branded from the herd:

To calculate the probability of one individual being branded from the herd, we need to consider the total number of horses in the herd and the probabilities for each type of horse being branded.

Total number of horses in the herd = Number of stallions + Number of mares + Number of foals = 10 + 15 + 20 = 45

The probability of one individual being branded can be calculated as follows:

Probability = (Number of stallions * Probability of a stallion being branded) + (Number of mares * Probability of a mare being branded) + (Number of foals * Probability of a foal being branded)

Probability = (10 * 0.2) + (15 * 0.3) + (20 * 0.6)

Probability = 2 + 4.5 + 12

Probability = 18.5

Therefore, the probability of one individual being branded from the herd is 18.5.

2) Probability of the captured horse being a stallion:

To find the probability of the captured horse being a stallion, we need to consider the total number of horses in the herd and the number of stallions in the herd.

Total number of horses in the herd = Number of stallions + Number of mares + Number of foals = 10 + 15 + 20 = 45

The probability of the captured horse being a stallion can be calculated as follows:

Probability = (Number of stallions / Total number of horses in the herd)

Probability = 10 / 45

Probability = 0.2222 (rounded to four decimal places)

Therefore, the probability of the captured horse being a stallion is approximately 0.2222.