If a coin is flipped 7 times, then what is the probability of getting 4 heads? – GeeksforGeeks

probability is a part of mathematics that deals with the hypothesis of happening of events. It is to forecast that what are the possible chances that the events will occur or the consequence will not occur. The probability as a act lies between 0 and 1 only and can besides be written in the shape of a percentage or fraction. The probability of probable event A is often written as P ( A ). here P shows the possibility and A shows the happen of an event. similarly, the probability of any event is much written as P ( ). When the end consequence of an event is not confirmed we use the probabilities of certain outcomes—how probably they occur or what are the chances of their happen. To understand probability more accurately we take an example as rolling a die : 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 consequence is an evenly 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 count 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 4 heads?

Solution:

Use the binomial distribution directly. Let us assume that the number of heads is represented by ten ( where a result of heads is regarded as success ) and in this case X = 4 Assuming that the coin is unbiased, you have a probability of success ‘ p ’ ( where phosphorus is considered as success ) is 1/2 and the probability of failure ‘ q ’ is 1/2 ( where q is considered as bankruptcy ). The number of trials is represented by the letter ’ n ’ and for this interview n = 7. now good use the probability function for a binomial distribution : P ( X = x ) = nCxpxqn-x Using the information in the problem we get P ( X = 4 ) = ( 7C4 ) ( 1/2 ) 4 ( 1/2 ) 3 = 35 × 1/16 × 1/8 = 35/128 Hence, the probability of flipping a coin 7 times and getting heads 4 times is 35/128 .

Similar Questions

Question 1: What is the probability of flipping a coin 20 times and getting 15 heads? Answer:

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

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( According to the binomial concept ) This gives us a total of 220 possibilities for flipping 20 coins. immediately, how many ways can we get 15 heads ? This is 20 choose 15, or ( 20C15 ) This means our probability is ( 20C15 ) /220 = 15504⁄1048576 ≈ .01478

Question 2: What is the probability of 3 heads in 3 coins tossed together.? Solution:

3 coin tosses. This means, total observations = 9 ( According to binomial concept ) Required result → 3 Heads { H, H, H } This can occur merely once ! therefore, required consequence = 1 Probability ( 3 Heads ) = ( 1⁄2 ) 3 = 1/8

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