Math Problem Statement

Three coins are tossed simultaneously. Find the probability of getting (i) at least 2 heads (ii) no heads

Solution

When three coins are tossed simultaneously, the possible outcomes are as follows:

{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}

There are 23=82^3 = 8 possible outcomes since each coin has two outcomes (head or tail) and there are three coins.

(i) Probability of getting at least 2 heads:

The outcomes where at least 2 heads appear are: {HHH,HHT,HTH,THH}\{HHH, HHT, HTH, THH\} There are 4 favorable outcomes. Hence, the probability is: P(at least 2 heads)=Number of favorable outcomesTotal outcomes=48=12P(\text{at least 2 heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{8} = \frac{1}{2}

(ii) Probability of getting no heads:

The only outcome where no heads appear is: {TTT}\{TTT\} There is 1 favorable outcome. Hence, the probability is: P(no heads)=Number of favorable outcomesTotal outcomes=18P(\text{no heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{8}


Would you like further details on any part of this problem?

Here are 5 related questions:

  1. What is the probability of getting exactly 1 head when tossing 3 coins?
  2. How many outcomes have at least 1 head in a 3-coin toss?
  3. If 4 coins are tossed, what is the probability of getting at least 2 heads?
  4. What is the probability of getting all tails when tossing 4 coins?
  5. How does the probability change if 5 coins are tossed simultaneously?

Tip: In probability, "at least" generally means you count all outcomes greater than or equal to a certain condition.

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

Probability of event = (Number of favorable outcomes) / (Total number of outcomes)

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8