A coin is tossed 7 times. Find the probability of getting GMAT Problem Solving

Question: A coin is tossed 7 times. Find the probability of getting more heads than tails in all 7 tosses?

A. ½
B. 63/128
C. 4/7
D. 61/256
E. 63/64

Answer: A

Solution and Explanation:

Approach Solution 1:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to probability. Because of how the options are set up, it is hard to choose the best one. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question
In the event that the coin is fair, P(H) = P(T) = ½
We can follow the suggestion made by the justification in your initial post:
Results in total: 2⁷
Favorable results include: 4 heads - a combination of HHHHTTT - 7!/(4!*3!) = 35 (number of permutations of 7 letters out of which 4 H's and 3 T's are similar);
5 heads - a combination of HHHHHTT - 7!/(5!*2!)=21;
and 6 heads - a combination of HHHHHTT - 7!/(6!*2!)=21;
7 heads, - a combination of HHHHHHH = 1;
6 heads - combination of HHHHHHT - 1; 6!/(6!*1!) = 7;
P(H>T)=Favorable results/Total results
(35+21+7+1)/2⁷ = ½
Correct option: A

Approach Solution 2:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to probability. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
There is a simpler way to address this question.
Since the probability of having either heads or tails is equal (1/2) and a tie in 7 (odd) tosses is not feasible
The probability of getting more heads than tails corresponds to the probability of getting more tails than heads, which is 1/2. How else?
Does the probability favor any of the tails or heads?
(The distribution of the probabilities is symmetrical:
P(H=7)=P(T=7), P(H=5)=P(T=5), ... also P(H>4)=P(T>4))
Correct option: A

Approach Solution 3:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to probability. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
First, we should think what are the probable outcomes when we toss a coin: head or tail (2 outcomes) (2 outcomes)
Now as the coin is fair, the probability that we will get a head or a tail is ½
To illustrate, let's take a smaller version of the preceding question:
What is the likelihood of getting more heads in 3 tosses?
1st case: We can get 3 heads: HHH
Probability of HHH = 1/2 * 1/2 * 1/2 = 1/8
Chance of getting 3 heads = 1/8
2nd case: There are 3 ways to get 2 heads : HHT, HTH, THH
Probability of getting 2 first heads (HHT) = 1/2 * 1/2 * 1/2 = 1/8
Probability of a tail between heads (HTH) = 1/2 * 1/2 * 1/2 = 1/8
Probability of two last heads (THH) = 1/2 * 1/2 * 1/2 = 1/8
Chance of getting 2 heads = 3* 1/8
As you can see HHT, HTH and THH are distinct configurations of HHT
Probability of getting 2 heads = (No. of configurations of HHT)* (Probability of receiving HHT) = 3!/2! * (1/2 * 1/2 * 1/2) = 3/8
Overall likelihood of receiving more heads in 3 tosses = 1/8 + 3/8 = 4/8 = ½
Correct option: A

“A coin is tossed 7 times. Find the probability of getting" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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