You might have noticed that before the commencement of a cricket match, a decision is to be made, which team would bat or bowl first. How is this done? You see that the captains of the two teams participate in a coin toss wherein they pick one side of a coin each, that is head or tail. The umpire tosses the coin in the air. The team which wins the toss gets to make the decision of batting or bowling first. This is one of the most common applications of the coin
toss experiment. Nội dung chính Show Why do you think this method is used? This is because the possibility of obtaining a Head in a coin toss is as likely as obtaining a tail, that is, 50%. So when you toss one coin, there are only two possibilities – a head (H) or a tail (L). However, what if you want to toss 2 coins simultaneously? Or say 3, 4 or 5 coins? The outcomes of these coin tosses will differ. Let us learn more about the coin toss probability formula. Probability is the measurement of chances – the likelihood that an event will occur. If the probability of an event is high, it is more likely that the event will happen. It is measured between 0 and 1, inclusive. So if an event is unlikely to occur, its probability is 0. And 1 indicates the certainty for the occurrence. Now if I ask you what is the probability of getting a Head when you toss a coin? Assuming the coin to be fair, you straight away answer 50% or ½. This is because you know that the outcome will either be head or tail, and both are equally likely. So we can conclude here: Number of possible outcomes = 2 Number of outcomes to get head = 1 Probability of getting a head = ½ Hence, \(\begin{array}{l}Probability\;of\;getting\;a\;head = \frac{No\;of\;outcomes\;to\; get\;head}{No\;of\;possible\;outcomes}\end{array} \) We can generalise the coin toss probability formula: \(\begin{array}{l}Probability\;of\;certain\;event=\frac{Number\;of\;favourable\;outcomes}{Total\;number\;of\;possible\;outcomes}\end{array} \) Solved ExamplesQuestion: Two fair coins are tossed simultaneously. What is the probability of getting only one head? Solution: When 2 coins are tossed, the possible outcomes can be {HH, TT, HT, TH}. Thus, the total number of possible outcomes = 4 So number of desired outcomes = 2 Therefore, probability of getting only one head \(\begin{array}{l}=\frac{Number\;of\;favourable\;outcomes}{Total\;number\;of\;possible\;outcomes}\end{array} \) \(\begin{array}{l}=\frac{2}{4}=\frac{1}{2}\end{array} \) Question: Three fair coins are tossed simultaneously. What is the probability of getting at least 2 tails? Solution: When 3 coins are tossed, the possible outcomes can be {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Thus, total number of possible outcomes = 8 So number of desired outcomes = 4 Therefore, probability of getting at least 2 tails = \(\begin{array}{l}\frac{No\;of\;favourable\;outcomes}{Total\;number\;of\;possible\;outcomes}\end{array} \) \(\begin{array}{l}=\frac{4}{8}=\frac{1}{2}\end{array} \) To solve more problems on the topic, download BYJU’S -The Learning App. Here we will learn how to find the probability of tossing three coins. Let us take the experiment of tossing three coins simultaneously: When we toss three coins simultaneously then the possible of outcomes are: (HHH) or (HHT) or (HTH) or (THH) or (HTT) or (THT) or (TTH) or (TTT) respectively; where H is denoted for head and T is denoted for tail. Therefore, total numbers of outcome are 23 = 8 The above explanation will help us to solve the problems on finding the probability of tossing three coins. Worked-out problems on probability involving tossing or throwing or flipping three coins: 1. When 3 coins are tossed randomly 250 times and it is found that three heads appeared 70 times, two heads appeared 55 times, one head appeared 75 times and no head appeared 50 times. If three coins are
tossed simultaneously at random, find the probability of: (i) getting three heads, (ii) getting two heads, (iii) getting one head, (iv) getting no head Solution: Total number of trials = 250. Number of times three heads appeared = 70. Number of times two heads appeared = 55. Number of times one head
appeared = 75. Number of times no head appeared = 50. In a random toss of 3 coins, let E1, E2, E3 and E4 be the events of getting three heads, two heads, one head and 0 head respectively. Then, (i) getting three heads P(getting three heads) = P(E1) Number of times three heads appeared = 70/250 = 0.28 (ii) getting two heads P(getting two heads) = P(E2) Number of times two heads appeared = 55/250 = 0.22 (iii) getting one head P(getting one head) = P(E3) Number of times one head appeared = 75/250 = 0.30 (iv) getting no head P(getting no head) = P(E4) Number of times on head appeared = 50/250 = 0.20 Note: In tossing 3 coins simultaneously, the only possible outcomes are E1, E2, E3, E4 and P(E1) + P(E2) + P(E3) + P(E4) = (0.28 + 0.22 + 0.30 + 0.20) 2. When 3 unbiased coins are tossed
once. What is the probability of: (i) getting all heads (ii) getting two heads (iii) getting one head (iv) getting at least 1 head (v) getting at least 2 heads (vi) getting atmost 2 heads Solution: In tossing three coins, the sample space is given by S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} And, therefore, n(S) = 8. (i) getting all heads Let E1 = event of
getting all heads. Then, (ii) getting two heads Let E2 = event of getting 2 heads. Then, (iii) getting one head Let E3 = event of getting 1 head. Then, (iv) getting at least 1 head Let E4 = event of getting at least 1 head. Then, (v) getting at least 2 heads Let E5 = event of getting at least 2 heads. Then, (vi) getting atmost 2 heads Let E6 = event of getting atmost 2 heads. Then, 3. Three coins are tossed simultaneously 250 times and the outcomes are recorded as given below.
If the three coins are again tossed simultaneously at random, find the probability of getting (i) 1 head (ii) 2 heads and 1 tail (iii) All tails Solution: (i) Total number of trials = 250. Number of times 1 head appears = 100. Therefore, the probability of getting 1 head = \(\frac{\textrm{Frequency of Favourable Trials}}{\textrm{Total Number of Trials}}\) = \(\frac{\textrm{Number of Times 1 Head Appears}}{\textrm{Total Number of Trials}}\)
= \(\frac{100}{250}\) = \(\frac{2}{5}\) (ii) Total number of trials = 250. Number of times 2 heads and 1 tail appears = 64. [Since, three coins are tossed. So, when there are 2 heads, there will be 1 tail also]. Therefore, the probability of getting 2 heads and 1 tail = \(\frac{\textrm{Number of Times 2 Heads and 1 Trial appears}}{\textrm{Total Number of Trials}}\)
= \(\frac{64}{250}\) = \(\frac{32}{125}\) (iii) Total number of trials = 250. Number of times all tails appear, that is, no head appears = 38. Therefore, the probability of getting all tails = \(\frac{\textrm{Number of Times No Head Appears}}{\textrm{Total Number of Trials}}\) = \(\frac{38}{250}\) = \(\frac{19}{125}\). These examples will help us to solve different types of problems based on probability of tossing three coins. Probability Probability Random Experiments Experimental Probability Events in Probability Empirical Probability Coin Toss Probability Probability of Tossing Two Coins Probability of Tossing Three Coins Complimentary Events Mutually Exclusive Events Mutually Non-Exclusive Events Conditional Probability Theoretical Probability Odds and Probability Playing Cards Probability Probability and Playing Cards Probability for Rolling Two Dice Solved Probability Problems Probability for Rolling Three Dice 9th Grade Math From Probability of Tossing Three Coins to HOME PAGE Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. What is the probability of getting 3 heads if 6 and 10 coins are tossed simultaneously?Probability of getting 3 heads : P(X=3)=6C(21)3(21)6−3=20×21=165. What is the probability of getting 3 heads in 10 tosses?Therefore P=1201024=15128≈11.7%. What is the probability of getting 3 heads when tossed?(i) Let E1 denotes the event of getting three heads. Hence the required probability is 0.28. What is the probability of getting 3 heads and 3 tails when 6 coins are tossed?So the answer is 20/64=5/16. What is the probability of 3 heads?Answer: If a coin is tossed three times, the likelihood of obtaining three heads in a row is 1/8. Let's look into the possible outcomes. The total number of possible outcomes = 8.
What is the probability of getting all heads if three coins are tossed simultaneously?Hence, the probability of getting all heads is 81.
What is the probability of getting a head in 3rd toss?Summary: A coin is tossed 3 times. The probability of getting at least one head is 7/8.
What is the probability of 3 coins landing on heads?For each coin toss, there will 2 outcomes. So by multiplying outcomes of each toss i.e., 2 × 2 × 2 = 8 total number of possible outcomes are obtained. So, there is 12.5% chances of getting all 3 heads when 3 coins are tossed.
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Three coins are tossed simultaneously what is the probability of getting 3 heads
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