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You are a space alien. You visit planet Earth and abduct $97$ chickens, $47$ cows, and $77$ humans. Then, you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected. $\newline$ Create a probability model to show how likely you are to select each type of Earth creature.

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Find probabilities using the addition rule

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Q. You are a space alien. You visit planet Earth and abduct

97

chickens,

47

cows, and

77

humans. Then, you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected.

\newline

Create a probability model to show how likely you are to select each type of Earth creature.

Define Total Creatures: Let's define the total number of creatures abducted: $\text{Total creatures} = \text{Number of chickens} + \text{Number of cows} + \text{Number of humans}$
Calculate Total Creatures: Now, let's calculate the total number of creatures: $\newline$ Total creatures = $97$ chickens + $47$ cows + $77$ humans $\newline$ Total creatures = $221$
Calculate Chicken Probability: Next, we will calculate the probability of selecting each type of creature. The probability is the number of creatures of a type divided by the total number of creatures.
Calculate Cow Probability: The probability of selecting a chicken $P(\text{Chicken})$ is: $P(\text{Chicken}) = \frac{\text{Number of chickens}}{\text{Total creatures}}$ $P(\text{Chicken}) = \frac{97}{221}$
Calculate Human Probability: The probability of selecting a cow $P(\text{Cow})$ is: $P(\text{Cow}) = \frac{\text{Number of cows}}{\text{Total creatures}}$ $P(\text{Cow}) = \frac{47}{221}$
Check Sum of Probabilities: The probability of selecting a human $P(\text{Human})$ is: $\newline$ $P(\text{Human}) = \frac{\text{Number of humans}}{\text{Total creatures}}$ $\newline$ $P(\text{Human}) = \frac{77}{221}$
Check Sum of Probabilities: The probability of selecting a human $P(\text{Human})$ is: $P(\text{Human}) = \frac{\text{Number of humans}}{\text{Total creatures}}$ $P(\text{Human}) = \frac{77}{221}$ Finally, we check if the sum of all probabilities equals $1$ , as it should in a probability model. $P(\text{Chicken}) + P(\text{Cow}) + P(\text{Human}) = \left(\frac{97}{221}\right) + \left(\frac{47}{221}\right) + \left(\frac{77}{221}\right)$ $P(\text{Chicken}) + P(\text{Cow}) + P(\text{Human}) = \frac{221}{221}$ $P(\text{Chicken}) + P(\text{Cow}) + P(\text{Human}) = 1$

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