Probability

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There are 52 cards in a deck with no jokers. There are 13 hearts in such a deck so the probability of drawing a heart is

13/52

There are 6 sides of a die, and rolling a 3 is one of the 6 sides.

Therefore, there are 5 sides on the die which is not a 3.

So, (outcomes wanted)/(total outcomes) = 5/6

A z-score gives the distance (specifically number of standard deviations) from the mean so when you compare z-scores, it gives a direct comparison of how far from the mean the values are.

Almost all statistical distribution have a mean. It is the expected value of the random variable which is distributed according to that function.

It is 10/52 = 5/26.

The probability of doing so, if the first card is not replaced, is 0.0385, approx.

The odds of a woman having twins on new years even where on baby is born in the final minutes of the year and the other born in the beginning minutes of the next year is considered a rarity and only a handful of cases are reported each year.

If you mean rolling at least one three, the 1/3.

If you mean exactly one three, then 5/18.

and

If you mean a sum of 3 for the two throws, the answer is 1/18

On a random draw of a single card, it is 16/52 = 4/13.

steam, mast, stem team, am, mat, met, at,as

Probability that it is one of these eight cards is 8/52. Hence the probability of not getting these eight cards is 44/52

It's human nature to think so, but no. Even after getting 100 heads in a row, the odds of the next flip being heads is still 50%.

The probability that you will toss five heads in six coin tosses given that at least one is a head is the same as the probability of tossing four heads in five coin tosses1.

There are 32 permutations of five coins. Five of them have four heads2. This is a probability of 5 in 32, or 0.15625.

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1Simplify the problem. It asked about five heads but said that at least one was a head. That is redundant, and can be ignored.

2This problem was solved by simple inspection. If there are four heads in five coins, this means that there is one tail in five coins. That fact simplifies the calculation to five permutations exactly.

From a well shuffled and complete deck without the Jokers, pulling one card and getting a heart or spade is one in two. Getting a spade is a one in four shot. (Four suits, equal number of cards in each suit....) Same for club, heart or diamond. Getting a spade or a heart is a one in four plus a one in four or one in two. It's fifty-fifty. The probability of drawing a heart or a spade when 1 card is picked up from a well shuffled (complete) deck (without Jokers) is 0.5 or one half.

Astigmatism old ages

an optimistic one

Two out of nine. 2:9.

THe answer will depend on whether the confidence interval is central or one-sided. If central, then

-1.28 < z < 1.28

-1.28 < (m - 18)/6 < 1.28

-7.68 < m - 18 < 7.68

10.3 < m < 25.7

If you consider that there on about 6 billion (6,000,000,000) people, give or take, on the Earth, and you assume an average sleep time of 8 hours, then two thirds of the population are up at any one time. This is about 4 billion people.

True.

P(club) + P(QS) 1/4 + 1/52 = .25 + .0192 = .269

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