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
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Calculate the 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 number of favorable outcomes \(n_1 = 2\). The probability of rolling a number less than 3, \(P(\text{number}<3)=\frac{2}{6}=\frac{1}{3}\)

Step2: Calculate the probability of the spinner landing on red

The spinner has 4 equal - sized sections (colors). The number of favorable outcomes for landing on red \(n_2 = 1\). The probability of the spinner 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, if \(A\) is the event of rolling a number less than 3 and \(B\) is the event of the spinner landing on red, then \(P(A\cap B)=P(A)\times P(B)\)
Substitute \(P(A)=\frac{1}{3}\) and \(P(B)=\frac{1}{4}\) into the formula: \(P(A\cap B)=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}\approx0.083\)

Answer:

The probability of the event is \(0.083\)