Probability

There are 4 suits in a deck of cards; each suit has a probability of being selected of 1/4. So, probability of a diamond is 1/4 or 0.25.

Two ways a die could be tested for fairness are empirical and analytic.

In the empirical method, you throw the die a large number of times and measure the distribution of the results - they should be evenly distributed within whatever level of tolerance (based on number of trials) that you want.

In the analytic method, you measure the dimensions of the die with extremely accurate equipment. This must include checks for physical symmetry and balance. Balance is checked with a balance beam that allows the die to be rotated about various axes to make sure the center of gravity is in the center of the die.

There is no such thing. The standard error can be calculated for a sample of any size greater than 1.

Each chance of a having a girl is 50% or 1/2. Three different children are separate events and so multiplying the chance all three together gives 1/2 x 1/2 x 1/2= 1/8. 1 in 8 chances will someone have three girls in a row.

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That depends on what numbers, I think

If you don't specify the color, there are four of each card. So out of 52 cards there are four nines. Four out of 52 can be simplified into 1/13, which is about 8%.

The statement of the question doesn't provide sufficient information to calculate that.

Subjective probability is defined as a person's own judgment of what is or is not going to happen, which does not consist of any kind of mathematical or calculated basis. One situation in which subjective probability would be a factor would be in the stock market. If a person felt that a certain stock would plummet and just had a feeling about it, and sold that stock away, that decision would have been based on subjective probability.

The answer depends on what game you are playing and so how many cards you are dealt!

Assuming that the four-sided spinner is fair and that it is numbered in the traditional way of 1, 2, 3 and 4, the probability of spinning a three is 1/4.

It is not possible to give a proper answer to the question for two main reasons. The first reason is that the probability of boys and girls are not equal. The global probability, at birth is 0.517 for boys and 0.483 for girls. Second, the children's genders are not independent events. Third, the gender ratios change with the parents' (mother's) age.

If you choose to ignore all these facts, then the probability is (1/2)4 = 1/16

It would depend on the parents' genes and age. Globally, the probability is approx 0.483

In general you cannot. You will need to know more about the distribution of the variable - you cannot assume that the distribution is uniform or Normal.

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It is 21/26.

There is no real relationship. Probabilities for the Normal distribution are extremely difficult to work out. The z-score is a method used to convert any Normal distribution into the Standard Normal distribution so that its probabilities can be looked up in tables easily.

There are infinitely many types of continuous probability distributions and the Normal is just one of them.

The probability of choosing a 10 is 4/52; likewise a Jack is 4/52. The probability of 10 or Jack is 4/52 + 4/52 = 8/52 or 2/13.

4

One each of Hearts , Diamonds, Clubs, and Spades.

There are 2597673 such hands.

There are 2597673 such hands.

William has 4 shirts that he can wear with a choice of 3 different pants. He has 12 different possible outcomes.

Why there are 12 possible outcomes: There are twelve possible outcomes because 4 multiplied by 3 is 12. This is called algorthim. Algorithm is when you multiply numbers to get your outcome.

There are plenty ways to get or find how many outcomes there are. These ways are a tree diagram, chart, sample spaces, ect.

Hope i helped! :)

No. Convenience sampling involves the active participation of the researcher. It's called convenience sampling because the researcher simply grabs whomever happens to be close to hand. It's not whether people volunteer themselves. Please see the link.

Time manage so you have slots to revise for each subject! :)