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If a coin is flipped 7 times, then what is the probability of getting 6 heads?

  • Last Updated : 30 Dec, 2021

Probability is a part of mathematics that deals with the possibility of happening of events. It is to forecast that what are the possible chances that the events will occur or the event will not occur. The probability as a number lies between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of likely event A is often written as P(A). Here P shows the possibility and A shows the happening of an event. Similarly, the probability of any event is often written as P(). When the end outcome of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occurring.

To understand probability more accurately we take an example as rolling a dice:

The possible outcomes are — 1, 2, 3, 4, 5, and 6.

The probability of getting any of the outcomes is 1/6. As the possibility of happening of an event is an equally likely event so there are same chances of getting any number in this case it is either 1/6 or 50/3%.

Formula of Probability

Probability of an event, P(A) = (Number of ways it can occur) ⁄ (Total number of outcomes)

Types of Events

  • Equally Likely Events: After rolling dice, the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 in fair dice rolling.
  • Complementary Events: There is a possibility of only two outcomes which is an event will occur or not. Like a person will play or not play, buying a laptop or not buying a laptop, etc. are examples of complementary events.

If a coin is flipped 7 times, then what is the probability of getting 6 heads?

Solution:

Use the binomial distribution directly. Let us assume that the number of heads is represented by x  (where a result of heads is regarded as success) and in this case X = 6

Assuming that the coin is unbiased, you have a probability of success ‘p’(where p is considered as success) is 1/2 and the probability of failure ‘q’ is 1/2(where q is considered as failure). The number of trials is represented by the letter ’n’ and for this question n = 7.

Now just use the probability function for a binomial distribution:

P(X = x) = nCxpxqn-x

U

the information in the problem we get

P(X = 6) = (7C6)(1/2)6(1/2)1 

= 7 × 1/64 × 1/2

= 7/128

Hence, the probability of flipping a coin 7 times and getting heads 6 times is 7/128.

Similar Questions

Question 1: What is the probability of flipping a coin 20 times and getting 10 heads?

Answer:

Each coin can either land on heads or on tails, 2 choices.  

(According to the binomial concept)

This gives us a total of 220 possibilities for flipping 20 coins.

Now how many ways can we get 10 heads? This is 20 choose 1

r (20C10)  

This means our probability is (20C10)/220= 184756⁄1048576 ≈ .1762

Question 2: What is the probability of 6 heads in 6 coins tossed together.?

Solution:

6 coin tosses. This means,

Total observations = 36(According to binomial concept)  

Required outcome → 6 Heads {H,H,H,H,H,H}

This can occur only ONCE!

Thus, required outcome = 1  

Probability (6 Heads) = (1⁄2)6 = 1/64

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