Question: A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?
- 1/16
- 1/2
- 3/16
- 11/16
- 3/8
Correct Answer: (D)
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- A fair coin is tossed 4 times
Find Out:
- The probability of getting at least 2 tails
Let us find the probability of the opposite circumstance and deduct the value from 1.
The opposite circumstance would be obtaining zero tails (i.e all heads) or 1 tail.
Therefore, we can say, P(HHHH)= (1/2)^4 =1/16
Now let’s multiply it by 4!/3!, then we get,
P(THHH)= 4!/3! ∗(1/2)^4 = 4/16
This is because the THHH scenario can occur in a number of ways: THHH, HTHH, HHTH, or HHHT.
It is required to note the fact that 4!/3! offers the number of arrangements of 4 letters THHH out of which 3 H's are equivalent.
Therefore, the probability of getting at least 2 tails = P(T≥2)=1−(1/16 + 4/16)= 11/16
Approach Solution 2:
The problem statement suggests that:
Given:
- A fair coin is tossed 4 times
Find Out:
- The probability of getting at least 2 tails
Let’s look for the probability of 2 tails, 3 tails and all 4 tails,
Therefore, we can say, P(TTTT)=((1/2)^4=1/16.
Now by multiplying by 4C3, we get,
P(HTTT)=(4!/3!)*(1/2)^4=4/16.
Since {4!/3!} provides the number of arrangements of 4 letters HTTT among which 3 T's are similar.
Then, P(TTHH) = 4C2*(1/2)^4 = 4!/2!*2!*(1/2)^4=6/16
Therefore, the total probability of getting at least 2 tails = 1/16 + 4/16 + 6/16 =11/16
Approach Solution 3:
The problem statement indicates that:
Given:
- A fair coin is tossed 4 times
Asked:
- Find out the probability of getting at least 2 tails
Since each toss directs to 2 results, then the total possibilities = 2^4= 16.
The pattern of obtaining no tail in 4 tosses = 1 (H H H H)
The pattern of obtaining 1 tail in 4 tosses = 4 (T H H H) (H T H H) ( H H T H) (H H H T)
Therefore, the patterns of obtaining at least two tails in 4 tosses = 16-5 = 11
Therefore, the probability of getting at least 2 tails = 11/16
“A fair coin is tossed 4 times. What is the probability of getting at''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions enable the candidates to access information and crack numerical problems. GMAT Quant practice papers assist the candidates to go through several sorts of questions that will enable them to enhance their mathematical understanding.
Suggested GMAT Problem Solving Questions
- An Octagon Is Inscribed In A Circle As Shown Above. What Of The Area GMAT Problem Solving
- In a Company of Only 20 Employees, 10 Employees make $80,000/yr GMAT Problem Solving
- A bag contains blue and red balls only GMAT Problem Solving
- (4.8*10^9)^(1/2) is closest in value to GMAT Problem Solving
- What Is The Units Digit Of 2222^333 ∗ 3333^222? GMAT Problem Solving
- If m=−2, What Is −m^(−m)? GMAT Problem Solving
- An Automated Manufacturing Plant Uses Robots To Manufacture Products GMAT Problem Solving
- The Surface Distance Between 2 Points on the Surface of a Cube is the GMAT Problem Solving
- When a Certain Perfect Square is Increased by 148, the Result is GMAT Problem Solving
- In How Many Ways Can One Divide 12 Different Chocolate Bars Into Four GMAT Problem Solving
- Employee X's Annual Salary Is $12,000 More Than Half Of Employee Y's GMAT Problem Solving
- What is the Area of Quadrilateral ABCD Shown? GMAT Problem Solving
- Eleven Chairs are Numbered 1 Through 11. Four Girls and Seven Boys GMAT Problem Solving
- Two Friends, Tanaya and Stephen were Standing Together GMAT Problem Solving
- If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 GMAT Problem Solving
- Barney is forming two large cubes, A and B, with small identical cubes GMAT Problem Solving
- It Takes Printer A 4 Minute More than Printer B to Print 40 GMAT Problem Solving
- A synchronized diving competition will feature 25 synchronized GMAT Problem Solving
- The Earth Travels Around The Sun At A Speed Of Approximately 18.5 miles GMAT Problem Solving
- There are 8 ounces in a 1/2 pound. How many ounces are in 7 3/4 lbs? GMAT Problem Solving
- In isosceles triangle EFG above, angle FEG measures 60 degrees GMAT Problem Solving
- In the Figure, O is the Center of the Circle. Which One of the Following GMAT Problem Solving
- If a and b are Positive Integers and (2a)^b= 2^3, What is the Value GMAT Problem Solving
- What is the Remainder When 3^243 is Divided by 5? GMAT Problem Solving
- A Fashion Designer Sold a Pair of Jeans to a Retail Store for 40 Percent GMAT Problem Solving
- A Rectangular-Shaped Carpet Remnant That Measures x Feet GMAT Problem Solving
- In The Figure Above, If The Square Inscribed In The Circle Has An Area GMAT Problem Solving
- A Right Triangle Is Inscribed In A Circle. The Legs Of The Triangle GMAT Problem Solving
- Tom and Jerry are running on the same road towards each other. If Tom GMAT Problem Solving
- A number is said to be prime saturated if the product of all the different GMAT Problem Solving
- What is the sum of first 10 non-negative even integers GMAT Problem Solving
- A certain computer program randomly generates equation of line is form GMAT Problem Solving
- A perfect number is one which is equal to the sum of all its positive GMAT Problem Solving
- At A Prestigious Dog Show, Six Dogs Of Different Breeds Are To Be GMAT Problem Solving
- The Average Wages of a Worker During a Fortnight Comprising 15 GMAT Problem Solving
- Which of the Following Fractions is the Largest? GMAT Problem Solving
- Alice and Bob Traveled in the Same Direction Along the Same Route at GMAT Problem Solving
- Paul, Quallis and Robert Divide a Sum of Money Among Themselves in the GMAT Problem Solving
- If A Sphere With Radius r Is Inscribed In A Cube With Edges Of Length GMAT Problem Solving
- A Globe Of Radius 8 Inches Is To Be Placed Into A Square Box For Shipment GMAT Problem Solving
- What is the sum of digits in decimal notation of number (10^20) - 16? GMAT Problem Solving
- Which of the following is equivalent to the pair of GMAT Problem Solving
- A password to a certain database consists of digits that can GMAT Problem Solving
- A Can do 1/3 of the Work in 5 Days and B Can do 2/5 of the Work in 10 Days GMAT Problem Solving
- The income of a broker remains unchanged though the rate of commission is increased GMAT Problem Solving
- Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving
- For the infinite sequence a1, a2, a3, ... an, an+1, an=3(an−1) for all GMAT Problem Solving
- The quantities S and T are positive and are related by the equation GMAT Problem Solving
- A child paints the six faces of a cube with six different GMAT Problem Solving
- In an opera theater. there are 300 seats available GMAT Problem Solving