Questions: Probability Word problem involving the probability of a union Fran the Fearless has a well-known act at a local zoo. As part of the act, Fran handles a scary animal that she picks at random out of the Box of Terror. The following animals are in the box: 11 poisonous snakes, 8 nonpoisonous snakes, 12 poisonous spiders, and 10 nonpoisonous spiders. What is the probability that the animal Fran picks is nonpoisonous or is a snake? Do not round intermediate computations, and round your answer to the nearest hundredth. (If necessary, consult a list of formulas.)

Probability Word problem involving the probability of a union Fran the Fearless has a well-known act at a local zoo. As part of the act, Fran handles a scary animal that she picks at random out of the Box of Terror. The following animals are in the box: 11 poisonous snakes, 8 nonpoisonous snakes, 12 poisonous spiders, and 10 nonpoisonous spiders. What is the probability that the animal Fran picks is nonpoisonous or is a snake? Do not round intermediate computations, and round your answer to the nearest hundredth. (If necessary, consult a list of formulas.)
Transcript text: Probability Word problem involving the probability of a union Fran the Fearless has a well-known act at a local zoo. As part of the act, Fran handles a scary animal that she picks at random out of the Box of Terror. The following animals are in the box: 11 poisonous snakes, 8 nonpoisonous snakes, 12 poisonous spiders, and 10 nonpoisonous spiders. What is the probability that the animal Fran picks is nonpoisonous or is a snake? Do not round intermediate computations, and round your answer to the nearest hundredth. (If necessary, consult a list of formulas.) $\square$
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Solution

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Solution Steps

To find the probability that the animal Fran picks is nonpoisonous or is a snake, we need to use the principle of inclusion and exclusion for probabilities.

  1. Calculate the total number of animals.
  2. Calculate the number of nonpoisonous animals.
  3. Calculate the number of snakes.
  4. Calculate the number of nonpoisonous snakes (since they are counted twice in the previous steps).
  5. Use the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).
Step 1: Total Number of Animals

The total number of animals in the Box of Terror is calculated as follows: \[ \text{Total Animals} = 11 + 8 + 12 + 10 = 41 \]

Step 2: Number of Nonpoisonous Animals

The number of nonpoisonous animals consists of nonpoisonous snakes and nonpoisonous spiders: \[ \text{Nonpoisonous Animals} = 8 + 10 = 18 \]

Step 3: Number of Snakes

The total number of snakes includes both poisonous and nonpoisonous snakes: \[ \text{Snakes} = 11 + 8 = 19 \]

Step 4: Number of Nonpoisonous Snakes

The number of nonpoisonous snakes is given as: \[ \text{Nonpoisonous Snakes} = 8 \]

Step 5: Probability Calculation

Using the principle of inclusion and exclusion, the probability that the animal Fran picks is nonpoisonous or is a snake is calculated as: \[ P(\text{Nonpoisonous or Snake}) = \frac{\text{Nonpoisonous Animals} + \text{Snakes} - \text{Nonpoisonous Snakes}}{\text{Total Animals}} = \frac{18 + 19 - 8}{41} = \frac{29}{41} \approx 0.7073 \]

Rounding this to the nearest hundredth gives: \[ P(\text{Nonpoisonous or Snake}) \approx 0.71 \]

Final Answer

\[ \boxed{0.71} \]

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