Question

a probability experiment consists of rolling a six - sided die and spinning the spinner shown at the right. the spinner is equally likely to land on each color. use a tree diagram to find the probability of the given event. then tell whether the event can be considered unusual. event: rolling a number less than 3 and the spinner landing on red the probability of the event is 0.083 (type an integer or decimal rounded to three decimal places as needed.) can the event be considered unusual? a. no, because the probability is not close enough to 1. b. no, because the probability is not close enough to 0. c. yes, because the probability is close enough to 1. d. yes, because the probability is close enough to 0.

Explanation:

Step1: Calculate probability of rolling a number less than 3

A six - sided die has 6 possible outcomes \(\{1,2,3,4,5,6\}\). The numbers less than 3 are 1 and 2. So the probability of rolling a number less than 3, \(P(\text{number}<3)=\frac{2}{6}=\frac{1}{3}\)

Step2: Calculate probability of spinner landing on red

The spinner has 4 equal - sized sections (colors). So the probability of landing on red, \(P(\text{red})=\frac{1}{4}\)

Step3: Use the multiplication rule for independent events

Since rolling a die and spinning a spinner are independent events, \(P(\text{number}<3\text{ and red})=P(\text{number}<3)\times P(\text{red})\)
Substitute the values: \(P=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}\approx0.083\)

Step4: Determine if the event is unusual

An event is considered unusual if its probability is close to 0. A probability of \(0.083\) is not close to 0 (an event with probability \(P\leq0.05\) is often considered unusual in some common probability cut - offs, but even by a less strict view, \(0.083\) is not close to 0)

Answer:

B. No, because the probability is not close enough to 0.