Question

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: 13 poisonous snakes, 9 nonpoisonous snakes, 11 poisonous spiders, and 4 nonpoisonous spiders. what is the probability that the animal fran picks is poisonous or is a snake?
do not round intermediate computations, and round your answer to the nearest hundredth.
(if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the total number of animals

The total number of animals is \(13 + 9+11 + 4=37\).

Step2: Calculate the number of poisonous animals

The number of poisonous animals is \(13+11 = 24\).

Step3: Calculate the number of snakes

The number of snakes is \(13 + 9=22\).

Step4: Calculate the number of poisonous snakes

The number of poisonous snakes is \(13\).

Step5: Use the formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Let \(A\) be the event that the animal is poisonous and \(B\) be the event that the animal is a snake.
\(P(A)=\frac{24}{37}\), \(P(B)=\frac{22}{37}\), \(P(A\cap B)=\frac{13}{37}\)
\(P(A\cup B)=\frac{24 + 22- 13}{37}=\frac{33}{37}\approx0.89\)

Answer:

\(0.89\)