Probability

The probability of drawing a diamond in a standard deck of cards is 1 in 4.

The probability of drawing a diamond if this is repeated 100 times is still 1 in 4, which translates to 25 in 100, but since this is a random process you would not expect diamonds exactly 25 times.

Pick 6 marbles. Weigh 3 against 3.

If they balance, then weigh the other two against each other to find the heavier one.

If they don't balance, look at the three that are heavier. Pick 2 and weigh them against each other. If they balance, then the 3rd marble in that group is the heavier one. If they don't balance, you have the heavier one.

These events are independent; so the probability of a girl is 0.5.

The probability is approx 0.81

Alpha or significance level is usually 0.1 or 0.05 for a 2-tailed test.

12 white marbles from (7+3+12) = 22 marbles

Chance of a white marble on first pick = 12/22 = 6/11.
Chance of a white marble on second and third picks are the same, as the marble is replaced.
So, the chance of a white marble three times is 6/11 * 6/11 * 6/11 = 216/1331 = approximately 16.23%

Without information about the bias, there can be no possible answer. You cannot even say that the probability of 4 is not 0.25 since suppose the spinner has the following probabilities:

Pr(1) = 0.1 Pr(2) = 0.4 Pr(3) = 0.25 Pr(4) = 0.25

is clearly biased - in favour of 2, but the probability of 4 is not affected by the bias.

8/33

1/7776

50/50, or one chance in each set of three rolls. No matter how many times it's rolled, every roll is one in six. Just like flipping a coin. it's 50/50 heads or tails, even if you got 'heads' 20 times in a row the next flip will still be 50/50 chance of 'heads' again

First calculate the probability of NOT getting a six. This probability is 5/6 x 5/6 ... x 5/6, i.e., (5/6) to the power 6. Then subtract 1 minus this probability. This gives you the probability of getting at least one six.

the probability 6o =1/6 = 60%

C1, C2, C3, C4


The number of combinations is 4 base 2, or 16.


There are 4 possible scenarios where you get 3 heads.




So the odds are 4:16, or 1:4.

2.82

Depends on what detail of outcome you are interested in. If you are only interested in the total, you can get all numbers between 5 (5 ones) and 30 (5 sixes) - a total of 26 different results.

Singular of "dice" is "die". Dice are usually constructed so that opposite numbers add up to 7.

In an ordinary 52 card deck, there are 4 three's, and 13 clubs, one of which is the 3 of clubs, so there are 16 cards that are a three or a club. The probability of drawing a three or a club is 16 out of 52, or 4 out or 13, or 0.308.

If it's like this:

"There are 4 books in a bag and two of the four are fiction. Jess randomly pulls one out of the bag and replaces it. What is the probability of getting two fiction books?"

Then you should do this, 2/4 x 2/4 = 4/16 or 1/4

If it's like this:

"There are 4 books in a bag and two of the four are fiction. Jess randomly pulls one out of the bag and doesn't replace it. What is the probability of getting two fiction books?"

Then you should do this, 2/4 x 1/3 = 2/12 or 1/6

110

For 6 sided dice, there is only 1 way to get a 2: (1,1). There are 36 outcomes rolling 2 dice; so the probability of rolling two numbers whose sum is 2 is 1/36.

There is no information on how many cars are on the road right now.

If 1 queen was drawn out of the 52 card deck without replacement, the probability of choosing a queen on the 2nd draw is 3/51 or 1/17.

motility

yes

It is true because the distribution is symmetrical about Z=0.