Question

A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear? (A) $\frac{3}{8}$ (B) $\frac{3}{7}$ (C) $\frac{5}{8}$ (D) $\frac{3}{4}$ (E) $\frac{7}{8}$

Name: Problem 38, Chapter :
Uploaded: 2019-09-01T15:11:22-08:00
Duration: 52 s
Channel: Dilip Paruchuri
Description: A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear? (A) (3)/(8) (B) (3)/(7) (C) (5)/(8) (D) (3)/(4) (E) (7)/(8)

   A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear?
(A) $\frac{3}{8}$
(B) $\frac{3}{7}$
(C) $\frac{5}{8}$
(D) $\frac{3}{4}$
(E) $\frac{7}{8}$

Instant Answer

Solved by Expert Dilip Paruchuri

09/01/2019

Step 1

This can be calculated as $2^3 = 8$, where 2 represents the two possible outcomes (head or tail) for each toss and 3 is the number of tosses. Show more…

Show all steps

Thanks for your feedback!

A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear? (A) $\frac{3}{8}$ (B) $\frac{3}{7}$ (C) $\frac{5}{8}$ (D) $\frac{3}{4}$ (E) $\frac{7}{8}$

Play audio

Feedback

Dilip Paruchuri and 78 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Conditional Probability

Conditional probability is a fundamental concept in probability theory that quantifies the likelihood of an event occurring given that another event has occurred. It is defined mathematically as P(A|B) = P(A ? B) / P(B), assuming P(B) > 0, and is crucial for analyzing situations where the occurrence of one event affects the probability of another.

Sample Space

The sample space in probability theory consists of all possible outcomes of an experiment. Defining the sample space accurately is essential for calculating probabilities, as it provides the context in which events are considered and analyzed.

Counting Principles

Counting principles involve methods such as the multiplication principle and combinations to enumerate the number of possible outcomes. These principles are key in determining the probabilities of events, particularly in discrete settings where outcomes can be systematically listed and counted.

Please give Ace some feedback