Question

probability of independent events independent practice use your understanding of probability and independent events to answer the questions below. 1. roberto will flip a coin and spin the spinner shown. a. make a tree diagram or list to represent the sample space. b. what is the probability the coin will land on tails and the spinner will land on a 4? c. what is the probability the coin will land on heads and the spinner will land on an odd number? 2. the table shows the snacks in mel’s pantry. snack amount granola bar 4 chips 3 fruit snack 5 what is the probability that she chooses a fruit snack, puts it back, and then chooses a granola bar? 3. mrs. williams has a prize box with different colored tickets as shown below. each ticket results in a different type of prize. 3 green tickets 4 yellow tickets 3 purple tickets pedro will randomly select a ticket, replace it, and then select another ticket. what is the probability that he chooses a yellow ticket and then a purple ticket? a. \\(\frac{3}{25}\\) b. \\(\frac{2}{15}\\) c. \\(\frac{4}{25}\\) d. \\(\frac{7}{20}\\) a car dealership has various combinations of vehicles in their car lot, all of which have an equally chance of being selected. mark each statement true or false. correct any false statements. a. there are 9 total possible outcomes. b. the probability of choosing a truck that is silver or black with a leather interior... the probability of choosing a sedan with cloth interior that is not red is \\(\frac{1}{24}\\).

Explanation:

Step1: Identify the spinner and coin outcomes

The coin has 2 outcomes (Heads, Tails). The spinner has 7 outcomes (1, 2, 3, 4, 5, 6, 7).

Step2: Determine the probability of each event

For the coin landing on Tails: \( P(\text{Tails}) = \frac{1}{2} \) (since there are 2 equally likely outcomes).
For the spinner landing on 4: \( P(4) = \frac{1}{7} \) (since there are 7 equally likely outcomes).

Step3: Multiply the probabilities (independent events)

Since the coin flip and spinner spin are independent, \( P(\text{Tails and 4}) = P(\text{Tails}) \times P(4) = \frac{1}{2} \times \frac{1}{7} = \frac{1}{14} \)

Answer:

\(\frac{1}{14}\)