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Probability

The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.

14,643 Questions

What is the probability that a 70 percent free throw shooter would make 1 of 2 shots?

The probability the shooter makes both shots is .7 * .7 = .49, and the probability of making neither is .3 * .3 = .09. So the probability of making exactly 1 out of 2 is 1 - .49 - .9 = .42, or 42 percent.

What is the definition for an equally likely outcome in the probability of an event?

http://www.emathzone.com/tutorials/basic-statistics/definition-of-probability.html

Two six sided dice are rolled what is the probabiliy for the sum to be greater than 4?

There are 36 equally-likely possibilities for a 2-dice roll (six possibilities for each die, multiplied together). Let's consider the probability of the sum being less than or equal to 4. There is only one way to roll a 2 (1+1), there are two ways to roll a 3 (1+2, 2+1), and three ways to roll a 4 (1+3, 2+2, 3+1). So there are 6 ways to roll at most a 4, meaning that there must be 36-6=30 ways to roll more than a 4. The probabiliity of rolling a sum greater than 4 is therefore 30/36, or 5/6.

Is the Z-test the same as Z-scores?

No, the Z-test is not the same as a Z-score. The Z-test is where you take the Z-score and compare it to a critical value to determine if the null hypothesis will be rejected or fail to be rejected.

Suppose the variance is 64 Find the standard deviation?

Standard deviation is the square root of the variance; so if the variance is 64, the std dev is 8.

The Associative Property does not work for which operations?

Subtraction and division.

While 2+ (3+4) = 2+ (4+3), the subtraction 2-(3-4) ≠ 2-(4-3). One yields 3 while the other yields 1.

Similarly, multiplication has this property while division does not.

Two coins and one six sided cube are tossed together What is the probability of getting 2 heads and a four?

Probability is defined as the number of ways an outcome can occur divided by the number of possible outcomes. For the coins, there are 4 outcomes (HH, HT, TH, TT). On the cube, there are 6 possible outcomes. The total number of outcomes is then 4*6 = 24. Since there is only 1 way to obtain HH, look at the cube outcomes. With the HH outcome, the cube would need to fall on a 4. So, there is only 1 way a HH4 can occur. Therefore the probability of getting 2 heads and a four is 1/24 or 0.04167.

How many cards must you draw from a regular deck of 52 playing cards to be sure at least 2 are from the same suit?

5. Assuming the first four are all different suits, the 5th card must be a duplicate suit. If any prior to the 5th card is not a new suit, it is garunteed to be a duplicate of a prior suit.

An event that will definitely happen is an event with what percent probability?

An event that will definitely happen is an event with 100% probability.

What is the probability of drawing 3 hearts in a row?

The probability of drawing 3 hearts in a row in a 52 card deck is 13/52 * 12/51 * 11/50 = 1716/132600 = 0.01294, or approximately 1 chance in 77.

What is the probability of drawing a king and a diamond from a deck of playing cards?

The probability of drawing a king is 4:52
The probability of drawing a diamond is 13:52 (or 1:4)
The probability of drawing a king (0.07692...) then replacing that king into the deck then drawing a diamond is 0.019230769.

If you leave the king out, the probability will be slightly greater (4/52) * (13/51)

Unless the king you left out of the deck was a king of diamonds, in which case, the probability would be (4/52) * (12/51)

Why event probabilities range from zero to one?

The probability of an event is the number of outcomes that are favourable to the outcome divided by the total number of outcomes. For continuous variables, it is the proportion of the outcome space, but the same argument applies.

The number of favourable outcomes must be non negative and so the probability has to be greater than or equal to 0. Also, the number of favourable outcomes can, at most, be as large as the total number so the probability must be less than or equal to 1.

How do you find the area to the right of the z-score?

Charts typically show and list the area to the left of the Z-Score value. To find the area to the right, just subtract the Z-Score value from 1; e.g. if the Z-Score value is .75 then take 1-.75 = .25.

Find two consecutive integers whose sum is 45?

First suppose the two consecutive integers bex and x+1then according to the situationx+x+1=452x+1=452x=45-12x=44x=44/2x=22now our assumed consecutive integers were x and x+1 , Now put x in itx=45x+1=45+1 =46Thus the Solution set is {(45,46)}

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