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What is the probability of obtaining 2 ones in a row when rolling a fair six sided die?
If you roll the die often enough, the probability of getting a 2 ones in a row is 1. In only 2 rolls, the answer is (1/6)*(1/6) = 1/36
What is the formula to find the probability?
Its not an exact thing like with circle radius, but basically add together all the numbers and make a fraction like if there are 3 yellow balls, 3 green ones and 5 blue ones in a bag, then you add 3+3+5 = 11, and then you figure out that the probability of picking a blue ball out of the bag is 5/11. Probability is the ratio of all outcomes that you define as being of interest divided by all possible outcomes. For example, the number of ways to get doubles on 2 6-sided dice is 6 (1,1 2,2, 3,3 4,4 5,5 6,6) but there are 36 different ways for the dice to turn up so the probability of getting doubles on a single roll is 6/36 = 1/6 Likewise there are 6 ways to roll a 7 (1,6 2,5 3,4 4,3 5,2 6,1) so the odds of rolling a seven on a single roll are 6/36 = 1/6 The math gets more involved as you start looking at situations where the odds of getting any one of the particular outcomes are not the same - for example, with loaded dice - or where you are looking at a sequence of events.
What is the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice?
Calculating getting a five on a dice:There are 6 sides to a dice so there would be 12 in a pair of dice. So you would have a 1 in 6 chance of rolling a 5.Calculating getting a sum of five:There are a total of 18 combinations you can get when rolling two dices. 1+1, 1+3, 1+4, 1+5, 1+6, 2+2, 2+3, 2+4, 2+5, 2+6, 3+3, 3+5, 3+6, 4+4, 4+5, 5+5, 6+4, and 6+6 (I eliminated ones which were equal to others such as eliminating 6+2 because it is the same as 2+6). Out of the combination of numbers, only two are able to sum up to five (2+3 and 1+4). This equals about an 11.1% chance of rolling two which equal 5 when added together.
What are the chances of having a girl after having 3 boys?
(assuming that the probability of having a girl or a boy is 50/50) Looking from beforehand, the probability of having three boys then a girl is the probability of each of these events happening multiplied together. That is 50% x 50% x 50% x 50% or 0.54 This would mean that the chance of having a girl after three boys is 0.0625. If you've already had the three boys though, it is a different story. The point is that previous experiences do not affect future ones; probability has no memory. Thus the probability of having a girl next is 50%, regardless of if you've had boys or girls in the past. To think otherwise is known as the gambler's fallacy, where a gambler says "black has come up 4 times in a row, it must be red next" even though the chance of red is always 50%
What is the probability of choosing a green marble from A jar containing 4 red 7 green and 5 blue marbles?
There are 16 marbles total and 7 green ones, so the probability is 7/16.
