There are 729 farmers in a state each having 6 animals each. The animals are either cows or hens. Previous year, the state faced a flood and the probability of survival of a hen was 1/3 and that of cow is 2/3. Find the number of families having 2 hens and 4 cows.
Answers
Step-by-step explanation:
this is the answer with explanation
Final answer: 240
The number of families having 2 hens and 4 cows is 240
Given: We are given,
no; of farmers= 729
no; of animals= 6
probability of survival of a hen= 1/3
probability of survival of a cow= 2/3
To find: We have to find the number of families having 2 hens and 4 cows
Explanation:
- Let us define the following events
H: An animal is a hen
C: An animal is a cow
E: A farmer having 4 cows and 2 hens
- First we have to choose the farmers have 4 cows and 2 hens.
- For solving this type of problems we use the combination method.
- Therefore probability of a family having 4 cows and 2 hens,
P(E)= (₆C₂ * 1/3 * 1/3) * (2/3 * 2/3 * 2/3 * 2/3)
= ₆C₂ * 16/729
= ((6 * 5)/(2 * 1)) * (16/729)
= 240/729
- Therefore expected number of a family having 4 cows and 2 hens,
= P(E) * total number of families
= (240/729) * 729
= 240
- Hence, we got the number of families having 2 hens and 4 cows is 240.
To know more about the concept please go through the links;
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