Math and Arithmetic
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# A die is rolled 5 times what is the probability of rolling exactly one 4?

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Possible outcomes of rolling a die 5 times = 6^5

Number of outcomes including rolling exactly one 4: 5^5 (5*5^4)

5^5/6^5 = 3125/7776 ~= 0.4019

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## Related Questions The probability of rolling a 6 is 1/6. The probability of rolling 10 times a 6 is (1/6)10 or 1.654X10-8. The probability of rolling a six is 1 out of 6, or 1/6. Now, perhaps your question is: If I roll a die 180 times, what is the probability of rolling a six at least once. This is the same as rolling a die 180 times and never once rolling a six. The probability is (5/6)180 which is 5.59 x 10-15. The probability of a one being rolled in a fair die is 1 in 6, or 0.1666... . The probability of a one not being rolled is 5 in 6, or 0.8333... . The probability, then, of exactly one one being rolled in nine rolls is 1 in 6 times 5 in 6 to the 8th power, or about 0.0388. The probability of rolling a 5, based on the information given, is 80/375 or 16/75. Your problem describes a relative frequency approximation of probability. Possible outcomes of rolling a die 5 times = 6^5 Number of outcomes including rolling exactly one 2: 5^5 (5*5^4) 5^5/6^5 = 3125/7776 ~= 0.4019 When a number cube is rolled twice, there are 36 possible outcomes. (1,1),(1,2),....(6,6). (3,3) occurs only once. Therefore, the probability of rolling a 3 both times is 1/36. The probability that 14 is rolled at least once is 1 - 5.5*10-32 which, for all intents and purposes, can be treated as 1. the chances of rolling doubles once is 1 in 6; 3 times in a row it is 1 in 216. It does not make any difference after how many times you rolled the dice before. The answer depends on how many times in total the dice are rolled. As the total number of rolls increases, the probability rolling a 6 and 4 three times in a row increases towards 1. The theoretical probability of rolling a 5 on a standard six sided die is one in six. It does not matter how many times you roll it, however, if you roll it 300 times, the theoretical probability is that you would roll a 5 fifty times. The probability of rolling a six is one in six. The probability of rolling three consecutive sixes is one in 216. (1/6 x 1/6 x 1/6 = 1/216)  The first roll doesn't matter for probability, it just sets the number to be rolled by the other two. So: P(rolling the same number three times) = P(rolling a particular number)2 = (1/6)2 = 1/36 (1/6)^3 since each event is independent and each has a probability of 1/6. Probability is a number between 0 and 1. The probability of an event cannot be 12.   There are two possibilities for rolling three once, so the probability of this even is 2/36 or 1/18. Since each roll is an independent event, the total probability is: P(rolling three three times) = (1/18)3 = 1/5832 Each roll of the die is a Bernoulli trial with a probability of success of 1/6 or about 0.1667. The probability of rolling a 3 exactly 18 times out of 50 is18 ~ Bin(50, 1/6), which equals(50!/(18!(50-18)!))(0.1667^18)(1-0.1667)^(50-18), which is about 0.00052. The probability of rolling at least one 2 when rolling a die 12 times is about 0.8878. Simply raise the probability of not rolling a 2 (5 in 6, or about 0.8333) to the 12th power, getting about 0.1122, and subtract from 1. If the coin is tossed and the die rolled sufficiently many times then the probability is 1: the event is a certainty.For just one toss and roll, the probability is 0.25 The probability of rolling a 6 on each roll of an unbiased cuboid die is 1/6 If you mean at least one of the rolls shows a 6 then it is the same as 1 - pr(no roll shows a 6) = 1 - (5/6)&#8310;&#8304; &asymp; 1 - 0.0000177 = 0.9999823 If you mean that exactly one 6 is rolled then: Pr(exactly one 6) = 60 &times; 1/6 &times; (5/6)&#8309;&#8313; &asymp; 0.0002130 The probability of rolling a 3 on each roll of an unbiased cuboid die is 1/6 If you mean at least one of the rolls shows a 3 then it is the same as 1 - pr(no roll shows a 3) = 1 - (5/6)&#8310;&#8304; &asymp; 1 - 0.0000177 = 0.9999823 If you mean that exactly one 3 is rolled then: Pr(exactly one 3) = 60 &times; 1/6 &times; (5/6)&#8309;&#8313; &asymp; 0.0002130 The probability of rolling doubles with 2 dice is 1 in 6, or about 0.1667. The probability of doing that 100 times in a row is 0.1667100 or about 1.531x10-78. The probability of rolling an odd number is 3/6 (or rather, 1/2), so the probability of rolling an odd number three times in a row is 1/2^3 is 1/8 or 12.5%.

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