What are the odds of flipping 7 heads in a row? – GeeksforGeeks

What are the odds of flipping 7 heads in a row ? A branch of mathematics that deals with the happen of a random event is termed probability. It is used in Maths to predict how likely events are to happen. The probability of any event can entirely be between 0 and 1 and it can besides be written in the form of a share.

The probability of event A is generally written as P(A). here P represents the possibility and A represents the event. It states how likely an consequence is about to happen. The probability of an event can exist alone between 0 and 1 where 0 indicates that consequence is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for certain i.e. certainty

If we are not indisputable about the result of an consequence, we take aid of the probabilities of certain outcomes—how likely they occur. For a proper sympathy of probability we take an exemplar as tossing a mint : There will be two potential outcomes—heads or tails. The probability of getting heads is half. You might already know that the probability is half/half or 50 % as the consequence is an evenly likely event and is complemental so the possibility of getting heads or tails is 50 %. Formula of Probability

Probability of an event, P(A) = Favorable outcomes / Total number of outcomes

Some Terms of Probability Theory

  • Experiment: An operation or trial done to produce an outcome is called an experiment.
  • Sample Space: An experiment together constitutes a sample space for all the possible outcomes. For example, the sample space of tossing a coin is head and tail.
  • Favourable Outcome: An event that has produced the required result is called a favourable outcome.  For example, If we roll two dice at the same time then the possible or favourable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).
  • Trial: A trial means doing a random experiment.
  • Random Experiment: A random experiment is an experiment that has a well-defined set of outcomes. For example, when we toss a coin, we would get ahead or tail but we are not sure about the outcome that which one will appear.
  • Event: An event is the outcome of a random experiment.
  • Equally Likely Events: Equally likely events are rare events that have the same chances or probability of occurring. Here The outcome of one event is independent of the other. For instance, when we toss a coin, there are equal chances of getting a head or a tail.
  • Exhaustive Events: An exhaustive event is when the set of all outcomes of an experiment is equal to the sample space.
  • Mutually Exclusive Events: Events that cannot happen simultaneously are called mutually exclusive events. For example, the climate can be either cold or hot. We cannot experience the same weather again and again.
  • Complementary Events: The Possibility of only two outcomes which is an event will occur or not. Like a person will eat or not eat the food, buying a bike or not buying a bike, etc. are examples of complementary events.

Some Probability Formulas

Addition rule: Union of two events, say A and B, then

P ( A or B ) = P ( A ) + P ( B ) – P ( A∩B ) P ( A ∪ B ) = P ( A ) + P ( B ) – P ( A∩B )

Complementary rule: If there are two possible events of an experiment so the probability of one event will be the Complement of another consequence. For case – if A and B are two possible events, then

P ( B ) = 1 – P ( A ) or P ( A ’ ) = 1 – P ( A ). P ( A ) + P ( A′ ) = 1 .

Conditional rule: When the probability of an event is given and the second is required for which first is given, then

P ( B, given A ) = P ( A and B ), P ( A, given B ). It can be frailty versa P ( B∣A ) = P ( A∩B ) /P ( A )

Multiplication rule: Intersection of two other events i.e. events A and B need to occur simultaneously. then

P ( A and B ) = P ( A ) ⋅P ( B ). P ( A∩B ) = P ( A ) ⋅P ( B∣A )

What are the odds of flipping 7 heads in a row?

Solution:

probability of an event = ( number of favorable event ) / ( total count of event ). P ( B ) = ( occurrence of Event B ) / ( total number of event ). probability of getting one point = 1/2. here Tossing a coin is an freelancer event, its not dependent on how many times it has been tossed. probability of getting 2 heads in a row = probability of getting head first time × probability of getting head second base time. probability of getting 2 headway in a row = ( 1/2 ) × ( 1/2 ) therefore, the probability of flipping 7 heads in a row = ( 1/2 ) 7

Similar Questions

Question 1: What are the chances of flipping 8 heads in a row? Solution:

probability of an event = ( phone number of friendly event ) / ( total phone number of event ). P ( B ) = ( occurrence of Event B ) / ( entire numeral of event ). probability of getting one head = 1/2 here Tossing a coin is an independent event, its not dependent on how many times it has been tossed. probability of getting 3 heads in a row = probability of getting head first base time × probability of getting capitulum second time x probability of getting mind third time

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probability of getting 3 mind in a row = ( 1/2 ) × ( 1/2 ) × ( 1/2 ) consequently, the probability of getting 8 heads in a course = ( 1/2 ) 8

Question 2: What are the chances of flipping 13 tails in a row? Solution:

probability of an event = ( number of friendly event ) / ( total numeral of event ) P ( B ) = ( happening of Event B ) / ( total number of consequence ) probability of getting one tail = 1/2 here if Tossing a mint is an freelancer event, its not dependent on how many times it has been tossed. probability of getting 3 tails in a course = probability of getting buttocks inaugural time × probability of getting tail second time x probability of getting tail third time probability of getting 3 tails in a course = ( 1/2 ) × ( 1/2 ) × ( 1/2 ) consequently, the probability of getting 13 tails in a row = ( 1/2 ) 13

Question 3: What is the probability of flipping a coin 14 times and getting 14 heads? Solution:

15 times mint tosses. This means, full observations = 215 ( According to binomial concept ) Required consequence → 20 Heads { H, H, H, H, H, H, H, H, H, H, H, H, H, H, H, H, H, H, H, H, } This can occur lone once ! huss, required result =1 now put the probability formula Probability ( 14 Heads ) = ( 1⁄2 ) 14 = 1⁄32768 Hence, the probability that it will constantly land on the HEAD slope will be, ( 1⁄2 ) 14 = 1⁄16384

Question 4: What are the chances of flipping 25 heads in a row? Solution:

probability of an event = ( number of favorable consequence ) / ( full number of event ). P ( B ) = ( happening of Event B ) / ( sum number of consequence ) probability of getting one head = 1/2 here Tossing a coin is an mugwump event, its not dependent on how many times it has been tossed. probability of getting 3 heads in a row = probability of getting question first base time × probability of getting heading second clock time x probability of getting steer third time probability of getting 3 headway in a row = ( 1/2 ) × ( 1/2 ) × ( 1/2 ) consequently, the probability of getting 25 heads in a row = ( 1/2 ) 25

My Personal Notes

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