We will be using the concept of probability to solve this. Show
Answer: The probability of flipping a coin three times and getting 3 tails is 1/8.Let's solve this step by step. Explanation: Let us mark H for Heads and T for Tails. The coin is flipped three times; the total number of outcomes = 2 × 2 × 2 = 8. Sample Space (|Ω|) = {(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)} = 8 Let X be the probability of getting all tails: X = {(T, T, T)} ⇒ |X| = 1 P(X) = |X| / |Ω| = 1/8. Thus, the probability of flipping a coin three times and getting 3 tails is 1/8.Relative Frequency Definition of ProbabilityThe relative frequency definition of probability says: If an experiment is repeated, the probability of an event (a specified outcome of the experiment) is the relative frequency of occurrence of that event in a large number of repetitions of the experiment. In this definition 'large number' is vague and will not be made precise here. The following links use the Virtual Laboratories in Probability and Statistics by Professor Kyle Siegrist of the University of Alabama at Huntsville. Each link opens a page that illustrates the relative frequency definition of probability for a different situation.
Sample Space Definition of Probability
How many possible outcomes are there if you toss a coin 3 times?There are eight possible outcomes of tossing the coin three times, if we keep track of what happened on each toss separately. In three of those eight outcomes (the outcomes labeled 2, 3, and 5), there are exactly two heads. This way of counting becomes overwhelming very quickly as the number of tosses increases.
What are the possible values of the random variable for the number of tails when you toss two coins?The possible values of the random variable X when n=2 is given as: X={0,1,2} X = { 0 , 1 , 2 } , where: 0 represents two tails. 1 represents one head.
What is the probability that all 3 tosses are tails?Answer: The probability of flipping a coin three times and getting 3 tails is 1/8.
What is the random variable of tossing 3 coins?When 3 coins are tossed, the possible outcomes are HHH, TTT, HTT, THT, TTH, THH, HTH, HHT. (i) Let E1 denotes the event of getting all tails. Hence the required probability is ⅛.
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