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.
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