The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. For example, the number of ways you can role a single die is 6, the number of ways to get an even number (2,4, or 6) is 3. So the probability of an even number is 3/6 or .5
3 coins can land in 8 different ways. Only one of these ways is all tails. So the probability of rolling at least one heads is 7/8 = 87.5% .
3
useing a punnett square shows two ways to express probability
There is a 1in 36 chance of rolling 2, a 2 in 36 chance of rolling 3 and a 3 in 36 chance of rolling 4. So there is a 30 in 36, or 5 in 6 chance of rolling at least 5 with a pair of fair dice. ------------------------------------------------------------ There is only 1 way of scoring 2 (1 and 1). 3 can be scored 2ways (1 & 3 and 3 & 1) 4 is possible 3 ways (1 & 3; 3 & 1; 2 & 2) 5 has 4 ways (1 & 4; 4 & 1; 2 & 3; 3 & 2) 6 has 5 ways (1 & 5; 5 & 1; 2 & 4; 4 & 2; 3 & 3) 7 has 6 ways (1 & 6; 6 & 1; 2 & 5; 5 & 2; 3 & 4; 4 & 3) 8 has 5 ways;9 has 4 ways; 10 has 3 ways; 11 has 2 ways; 12 has only 1 way. That totals 36 possible ways of scoring with two dice. So score 2 has probability 1/6; 3 has probability 2/6 = 1/3; 4 has probability 3/6 = 1/2; 5 has probability 4/6 = 2/3. We want to know the probability of scoring less than 5, which has 6 ways out of 36 = 1/6 Now, all the probabilities must total exactly 1, so the probability of scoring at least 5 must be 1 - 1/6 which is 5/6 = 0.83333333333 (the 3 reoccurs ) = 83.33333(recurring)% or just over 83%
The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. For example, the number of ways you can role a single die is 6, the number of ways to get an even number (2,4, or 6) is 3. So the probability of an even number is 3/6 or .5
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The probability of one event or the other occurring is the probability of one plus the probability of the other. The probability of getting 3 heads is the probability of 3 heads (1/23) multiplied by the probability of 4 tails (1/24) multiplied by the number of possible ways this could happen. This is 7c3 or 35. Thus the probability of 3 heads is 0.2734375. The probability of 2 tails is the probability of 2 tails (1/22) multiplied by the probability of 5 heads (1/25) multiplied by the number of ways this could happen. That is 7c5 or 21. Thus the probability of 2 tails is 0.1640625 The probability of one or the other is the sum of their probabilities: 0.1640625 + 0.2734375 = 0.4375 Thus the probability of getting 3 heads or 2 tails is 0.4375.
3 coins can land in 8 different ways. Only one of these ways is all tails. So the probability of rolling at least one heads is 7/8 = 87.5% .
3
useing a punnett square shows two ways to express probability
There is a 1in 36 chance of rolling 2, a 2 in 36 chance of rolling 3 and a 3 in 36 chance of rolling 4. So there is a 30 in 36, or 5 in 6 chance of rolling at least 5 with a pair of fair dice. ------------------------------------------------------------ There is only 1 way of scoring 2 (1 and 1). 3 can be scored 2ways (1 & 3 and 3 & 1) 4 is possible 3 ways (1 & 3; 3 & 1; 2 & 2) 5 has 4 ways (1 & 4; 4 & 1; 2 & 3; 3 & 2) 6 has 5 ways (1 & 5; 5 & 1; 2 & 4; 4 & 2; 3 & 3) 7 has 6 ways (1 & 6; 6 & 1; 2 & 5; 5 & 2; 3 & 4; 4 & 3) 8 has 5 ways;9 has 4 ways; 10 has 3 ways; 11 has 2 ways; 12 has only 1 way. That totals 36 possible ways of scoring with two dice. So score 2 has probability 1/6; 3 has probability 2/6 = 1/3; 4 has probability 3/6 = 1/2; 5 has probability 4/6 = 2/3. We want to know the probability of scoring less than 5, which has 6 ways out of 36 = 1/6 Now, all the probabilities must total exactly 1, so the probability of scoring at least 5 must be 1 - 1/6 which is 5/6 = 0.83333333333 (the 3 reoccurs ) = 83.33333(recurring)% or just over 83%
The probability is 3/8.The probability is 3/8.The probability is 3/8.The probability is 3/8.
The sums divisible by 3 are 3, 6, 9 and 12. These can be obtained in 2, 5, 4 and 1 ways respectively, giving 2 + 5 + 4 + 1 = 12 ways of success. There are 36 possible ways two dice can fall → probability = ways_of_success/possible_ways = 12/36 = 1/3.
On a standard pair of six-sided dice, there are two ways to roll a "3"; i.e., a "1" and a "2" or a "2" and a "1". There are 36 possible outcomes. Therefore, the probability of rolling exactly 3 is 2/36, which equals 1/18. The probability of rolling 3 or higher is 35/36. The probability of rolling 3 or lower is 3/36, which is 1/12.
Yes- the highest probability value is the mode. Let me clarify this answer: For a probability mass function for a discrete variables, the mode is the value with the highest probability as shown on the y axis. For a probability density function for continuous variables, the mode is the value with the highest probability density as shown on the y-axis.