Question

you spin each spinner in the diagram one time. what is the probability that the first two spinners land on 1? enter the answer in each space provided. use numbers instead of words. p(1 on 1st spinner) = \boxed{} p(1 on 2nd spinner) = \boxed{} p(any number on 3rd spinner) = \boxed{} (sample problem: \shell game\ consists of placing three opaque cups, representing shells, upside down on a table and hiding a ball under one the cups. a player, who has not seen where the ball is hidden, has to choose one of the cups. if the ball is hidden under it, the player wins. what is the probability that the player will win 5 times in a row?)

Explanation:

For \( P(1 \text{ on 1st spinner}) \):

Step1: Determine total sections on 1st spinner

The first spinner has 6 equal - sized sections (labeled 1, 2, 3, 4, 5, 6).

Step2: Calculate probability of landing on 1

The probability of an event is given by the formula \( P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). For landing on 1, the number of favorable outcomes is 1 (since there is one section labeled 1) and the total number of outcomes is 6. So \( P(1 \text{ on 1st spinner})=\frac{1}{6} \).

For \( P(1 \text{ on 2nd spinner}) \):

Step1: Determine total sections on 2nd spinner

The second spinner is divided into 4 equal - sized sections (labeled 1, 2, 3, 4).

Step2: Calculate probability of landing on 1

Using the probability formula \( P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \), the number of favorable outcomes for landing on 1 is 1 and the total number of outcomes is 4. So \( P(1 \text{ on 2nd spinner})=\frac{1}{4} \).

For \( P(\text{any number on 3rd spinner}) \):

Step1: Understand the nature of the event

The event of landing on any number on the third spinner is a certain event. A certain event has a probability of 1, because no matter where the spinner lands, it will land on a number (the third spinner has numbers from 1 to 12, so all possible outcomes are favorable for the event "landing on any number").

Step2: Calculate the probability

For a certain event, \( P(\text{any number on 3rd spinner}) = 1 \).

Answer:

s:
\( P(1 \text{ on 1st spinner})=\boldsymbol{\frac{1}{6}} \)
\( P(1 \text{ on 2nd spinner})=\boldsymbol{\frac{1}{4}} \)
\( P(\text{any number on 3rd spinner})=\boldsymbol{1} \)