Questions: Olive has 3 fair coins. She will toss each coin one time. What is the probability that all 3 coins will land with "heads" facing up? A 1/2 B 1/4 C 1/6 D 1/8

Olive has 3 fair coins. She will toss each coin one time. What is the probability that all 3 coins will land with "heads" facing up? A 1/2 B 1/4 C 1/6 D 1/8
Transcript text: Olive has 3 fair coins. She will toss each coin one time. What is the probability that all 3 coins will land with "heads" facing up? A $\frac{1}{2}$ B $\quad \frac{1}{4}$ C $\quad \frac{1}{6}$ D $\quad \frac{1}{8}$
failed

Solution

failed
failed

Solution Steps

Step 1: Understand the problem

Olive has 3 fair coins, and she will toss each coin one time. We need to find the probability that all 3 coins will land with "heads" facing up.

Step 2: Determine the probability of a single coin landing on heads

Since each coin is fair, the probability of a single coin landing on heads is: \[ P(\text{Heads}) = \frac{1}{2} \]

Step 3: Calculate the probability of all 3 coins landing on heads

Since the coin tosses are independent events, the probability of all 3 coins landing on heads is the product of the probabilities of each individual coin landing on heads: \[ P(\text{All Heads}) = P(\text{Heads}) \times P(\text{Heads}) \times P(\text{Heads}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]

Final Answer

The probability that all 3 coins will land with "heads" facing up is: \[ \boxed{\frac{1}{8}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
How did the California voters' approval of Proposition 289 in November 1996 amend the state's constitution? It expanded antidiscrimination protection to include sexual orientation. It made it unlawful for the state to use race, sex, color, ethnicity, or national origin as a reason to either discriminate against or grant preferential treatment to anyone. It gave the governor additional powers to enforce antidiscrimination legislation. It included a provision formally sanctioning.
failedAnswered
Which situation is an example of comparative advantage in an international market? O Country A decides to grow extra potatoes so they have more to export, while Country B does not grow potatoes to export. O Factories in Country A and Country B produce the same number of tablet computers, Country A's factories could be used instead to build more laptops than the factories in Country B. O Country A invests in a new technology while Country B chooses to invest in education. O Country A can produce 100 units of rice per acre of farmland, while Country B can only produce 70 units of rice per acre of farmland using the same resources.
failedAnswered
A tree is 120 feet ( ft ) tall. How many inches (in) is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation. Ratios: 36 in/1 yd 1 ft/12 in = in ft yd mi in
failedAnswered
Find the values of (x) and (y) in each of the following triangles. 1. (x=x quad y=x sqrt2) 2. (x=22.5 quad y=45)
failedAnswered
Find the amount of the following ordinary annuities rounded to the nearest cent. Find the total interest earned. Amount of each deposit Deposited Rate Time (Years) Amount of an Annuity Interest Earned ------------------ 700 semiannually 12% 12 Click the icon to view the Amount of an Annuity Table. The amount of the annuity is approximately (Round to the nearest cent as needed.)