Whats the probability of getting an odd number and a tail when a die is rolled and a coin is tossed simultaneously?
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The probability of some event happening is a mathematical (numerical) representation of how likely it is to happen, where a probability of 1 means that an event will always happen, while a probability of 0 means that it will never happen. Classical probability problems often need to you find how often one outcome occurs versus another, and how one event happening affects the probability of future events happening. When you look at all the things that may occur, the formula (just as our coin flip probability formula) states that probability = (no. of successful results) / (no. of all possible results). Take a die roll as an example. If you have a standard, 6-face die, then there are six possible outcomes, namely the numbers from 1 to 6. If it is a fair die, then the likelihood of each of these results is the same, i.e., 1 in 6 or 1 / 6. Therefore, the probability of obtaining 6 when you roll the die is 1 / 6. The probability is the same for 3. Or 2. You get the drill. If you don't believe me, take a dice and roll it a few times and note the results. Remember that the more times you repeat an experiment, the more trustworthy the results. So go on, roll it, say, a thousand times. We'll be waiting here until you get back to tell us we've been right all along. But what if you repeat an experiment a hundred times and want to find the odds that you'll obtain a fixed result at least 20 times? Let's look at another example. Say that you're a teenager straight out of middle school and decide that you want to meet the love of your life this year. More specifically, you want to ask ten girls out and go on a date with only four of them. One of those has got to be the one, right? The first thing you have to do in this situation is look in the mirror and rate how likely a girl is to agree to go out with you when you start talking to her. If you have problems with assessing your looks fairly, go downstairs and let your grandma tell you what a handsome, young gentleman you are. So a solid 9 / 10 then. As you only want to go on four dates, that means you only want four of your romance attempts to succeed. This has an outcome of 9 / 10. This means that you want the other six girls to reject you, which, based on your good looks, has only a 1 / 10 change of happening (The sum of all events happening is always equal to 1, so we get this number by subtracting 9 / 10 from 1). If you multiply the probability of each event by itself the number of times you want it to occur, you get the chance that your scenario will come true. In this case, your odds are 210 * (9 / 10)4 * (1 / 10)6 = 0.000137781, where the 210 comes from the number of possible fours of girls among the ten that would agree. Not very likely to happen, is it? Maybe you should try being less beautiful!  Text Solution Solution : The sampe space (for a coin)
Solution: We use the basic concepts of probability to find the required outcomes. (i) Incorrect If two coins are tossed simultaneously then, Total possible outcomes are (H, H), (T, T), (H, T), (T, H) = 4 Number of outcomes to get two heads = (H, H) = 1 Number of outcomes to get two tails = (T, T) = 1 Number of outcomes to get any one of each = (H, T), (T, H) = 2 probability of getting two heads = Number of possible outcomes/Total number of favourable outcomes = 1/4 probability of getting two tails = Number of possible outcomes/Total number of favourable outcomes = 1/4 probability of getting one of each = Number of possible outcomes/Total number of favourable outcomes = 2/4 = 1/2 It can be observed that the probability of each of the outcomes is not 1/3. (ii) Correct Total number of possible outcomes when a die is thrown = (1, 2, 3, 4, 5, 6) Number of possible outcomes to get an odd number (1, 3, 5) = 3 Number of possible outcomes to get an even number (2, 4, 6) = 3 probability of getting odd number = Number of possible outcomes/Number of favourable outcomes = 3/6 = 1/2 Thus, the probability of getting an odd number is 1/2. Check out more about terms of probability. ☛ Check: NCERT Solutions for Class 10 Maths Chapter 15 Video Solution: Which of the following arguments are correct and which are not correct? Give reasons for your answer. (i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 (ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 25 Summary: The argument (i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 is incorrect and the argument (ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.is correct ☛ Related Questions:
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A coin is tossed and a die rolled. Find the probability of getting a head and an odd number. The answer is $\frac{1}{4}$. My reasoning is that rolling an odd number is $\frac{1}{2}$, and tossing a coin on heads is $\frac{1}{2}$. So $0.5 \times 0.5$ = $\frac{1}{4}$. Is this basically it?
Answer: The coin and die are independent, so the probabilities of the two events can be multiplied. The probability of an odd number is 1/2, and the probability of a tail is also 1/2, so the probability of both occurring is the product, 1/4. Step-by-step explanation: Let A be the event that the coin comes up tails. Let B be the event that the die comes up odd numbered. We can express the probability of both events happening, P(A,B) , as P(A,B)=P(A|B)P(B) , by the law of conditional probability. Assuming that the coin and die are fair and independent, then P(A|B)=P(A) , by the definition of independence. Thus, P(A,B)=P(A)P(B) . The probability the coin is tails is P(A)=12 , because each side is equally like (i.e., coin is fair). The probability the die come up odd is P(B)=12 , because the total set of outcomes, (1,2,3,4,5,6) has three such numbers and all outcomes are equally likely (i.e., die is fair). As a result, P(A,B)=P(A)P(B)=1212=14 . |
