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 B is often written as P(B). Here P shows the possibility and B show 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. Show
Though probability started with a gamble, in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc., it has been used carefully. 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 some chances of getting any number in this case it is either 1/6 or 50/3%. Formula of Probability
Types of Events
If a coin is tossed 5 times, what is the probability that it will always land on the same side?Solution:
Similar QuestionsQuestion 1: What is the probability of flipping 5 coins on the Tails side? Solution:
Question 2: What is the probability of flipping 4 coins on the Head’s side? Solution:
Question 3: What is the probability of flipping 3 coins on the Tails side? Solution:
In this article, we will learn how to find the probability of tossing 3 coins. We know that when a coin is tossed, the outcomes are head or tail. We can represent head by H and tail by T. Now consider an experiment of tossing three coins simultaneously. The possible outcomes will be HHH, TTT, HTT, THT, TTH, THH, HTH, HHT. So the total number of outcomes is 23 = 8. The above explanation will help us to solve the problems of finding the probability of tossing three coins. The probability of an event E is defined as P(E) = (Number of favourable outcomes of E)/ (total number of possible outcomes of E). Step by Step Solutions to the tossing of 3 coins ProblemsThe following are some problems related to the tossing of 3 coins. Example 1. When 3 unbiased coins are tossed once. Find the probability of: (i) getting all tails (ii) getting two heads (iii) getting at least 1 head (iv) getting one head Solution: When 3 coins are tossed, the possible outcomes are HHH, TTT, HTT, THT, TTH, THH, HTH, HHT. The sample space is S = { HHH, TTT, HTT, THT, TTH, THH, HTH, HHT} Number of elements in sample space, n(S) = 8 (i) Let E1 denotes the event of getting all tails. E1 = {TTT} n(E1) = 1 P(getting all tails) = n(E1)/ n(S) = ⅛ Hence the required probability is ⅛. (ii) Let E2 denotes the event of getting two heads. E2 = {HHT, HTH, THH} n(E2) = 3 P(getting two heads) = n(E2)/ n(S) = 3/8 Hence the required probability is ⅜. (iii) Let E3 denotes the event of getting atleast one head. E3 = { HHH, HTT, THT, TTH, THH, HTH, HHT } n(E3) = 7 P(getting atleast one head) = n(E3)/ n(S) = 7/8 Hence the required probability is 7/8. (iv) Let E4 denotes the event of getting one head. E4 = { HTT, THT, TTH} n(E4) = 3 P(getting one head) = n(E4)/ n(S) = 3/8 Hence the required probability is 3/8. Example 2: In an experiment, three coins are tossed simultaneously at random 250 times. It was found that three heads appeared 70 times, two heads appeared 55 times, one head appeared 75 times and no head appeared 50 times. find the probability of: (i) getting three heads, (ii) getting one head, (iii) getting no head (iv) getting two heads, Solution: The total number of trials, n(S) = 250 (i) Let E1 denotes the event of getting three heads. n(E1) = 70 P(E1) = No. of times 3 heads appeared/ total number of trials = n(E1) / n(S) = 70/250 = 0.28 Hence the required probability is 0.28. (ii) Let E2 denotes the event of getting one head. n(E2) = 75 P(E2) = No. of times 1 head appeared/ total number of trials = n(E2) / n(S) = 75/250 = 0.3 Hence the required probability is 0.3. (iii) Let E3 denote the event of getting no head. n(E3) = 50 P(E3) = No. of times no head appeared/ total number of trials = n(E3) / n(S) = 50/250 = 0.2 Hence the required probability is 0.2. (iv) Let E4 denote the event of getting 2 heads. n(E4) = 55 P(E4) = No. of times 2 heads appeared/ total number of trials = n(E4) / n(S) = 55/250 = 0.22 Hence the required probability is 0.22. Related Links:
Frequently Asked QuestionsThe possible outcomes are HTT, THT, TTH, THH, HTH, HHT, HHH, and TTT. When 3 coins are tossed, the number of outcomes = 23 = 8. When 3 coins are
tossed, the favourable outcome is HHH. When 3 coins are tossed together the probability of getting 2 tails is?Probability of getting at least two tails =84=21.
What is the probability that 2 tails will appear?The probability of two tails is P(TT) = 1/4 = 0.25. The probability of one head and one tail is P(H and T) = 2/4 =0.50.
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A coin was tossed three times, what is the probability the coin landed two tails up
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