Probability

The probability mass function is used to characterize the distribution of discrete random variables, while the probability density function is used to characterize the distribution of absolutely continuous random variables.

You might want to read more about this at www.statlect.com/prbdst1.htm

(see the link below or on the right)

Since there are 13 spades and 52 cards, the probability is 13/52 or 1/4=.25

13/52 or 1/4 (25%)

Sample Space: Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King.

To solve this problem you: 1) Find all factors of 24 (there are 6 factors- 1,24,6,4,2,12) 2) You elemenate all numbers that are not on a six sided die (24,12) 3) Now use probability. The die is numbered 1-6 and you have numbers 1,2,4 and 6 which makes 4 out of 6. 4) This last step I can't show you, so I'll have to explain. You set up a proportion box. Write the 4 over the 6 on one side and next to the 6 write the 96. Over the 96 write N, which will represent the answer to your equation. Then multiply 4 times 96 and divide the product by 6. If you followed these steps you should get an answer of 64.

hypergeometric distribution: f(k;N,n,m) = f(5;52,13,5)

The probability of tails on the next toss is 1/2=.5 since this event is INDEPENDENT of the prior events.

If the two marbles are drawn without replacement, the probability is 16/33.

If you pick from each of the possible letters at each stage, then there are 5 possible options for the first letter. Then there are 4 possible options for the second. Then there are 3 possible options for the 3rd and so on. This leaves us with 5x4x3x2 = 120 different arrangements. However, each arrangement has been counted twice, as it doesn't matter which way around the Os go. So to get the true answer, we need to divide by 2. 120/2 = 60, and therefore the number of different arrangements of the letters in the word COLOR is 60.

We need to find two things. FIrst we need to know how many ways there are to roll a 3 and second we need to look at how many total events (the sample space) there are. So we could get a 3 with a 1 and 2 or a 2 and 1. Since we are rolling 2 dice we can't have 3 and 0 since we cant roll a 0. So there are 2 ways to get 3. Now Each die has 6 different outcomes when we roll it so using the multiplication law, we hae 36 possible outcomes. Of these 2 give us a sum of 3 so that is 2/36 or 1/18

The domain of the normal distribution is infinite.

The only way to get a 12 is to get two sixes. The chance of rolling a six is 1/6 and chance of rolling two sixes is 1/36 or about 2.78%

If A and B are mutually exclusive, P(A or B)=P(A) + P(B)

They both cannot occur together.

For example: A die is rolled. A = an odd number; B= number is divisible by 2.

P(A or B) = 1/3 + 1/3 = 2/3

I haven't heard of a component with regards to statistics. If, by chance, you are referring to the complement, it is the probability that the event does not occur. In this case, the complement would be 0.58.

There are 2 red jacks, so 2/52 or about .038%

There are 180 different arrangements, you may punch in 6! to your calculator and get 720 and think this is right but you have to take into account that "d" and "o" and doubled, so, the arrangements will give you a different answer.

6*5*4*3*2*1/4= 180

180 arrangements. :)

This is a conditional probability, given the card is red, what is the chance it is a heart. Since there are 2 red hearts, the probability if 1/2

0.20 + 0.80*0.80

that would be = 1/221

= (4/52)(4/51)(3/4)

56%

as 100/50=2 so you times 28 by 2 to get 56%

Independent Events

2 out of 52

The probability is the ratio of the area of the shaded area to the area of the whole figure.

These are all independent events (flipping a coin will not affect the probability of drawing a Jack) so you can get the probability of all events occurring by multiplying together the probabilities of each event occurring. In other words: P (4 or 6, 2 heads, Jack) = P(4 or 6) * P(2 Heads) * P(Jack) Now we need to look at each probability separately. Remember that: Probability = Successful Outcomes / (Successful Outcomes + Unsuccessful Outcomes) In the case of rolling a die, a successful outcome (as defined in the problem) is rolling a 4 or 6. An unsuccessful outcome is everything else (1, 2, 3, or 5). Using the formula above then: Probability (4 or 6) = 2/6 = .33 Figuring out the probability of rolling two heads is slightly different because we are talking about two flips not one. In this case we have to go back to our original formula for multiple events. Probability (2 Heads) = Prob(Head) * Prob(Head) Since we know a coin-toss has a 1/2 chance of being heads or tails: Probability (2 Heads) = .5 * .5 = .25 Finally, in the case of picking up a card from a deck, a successful outcome (as defined in the problem) is picking a Jack. There are 4 Jacks in a standard deck so there are 4 possibilities of a successful outcome. There are 48 cards in a stardard deck that are not Jacks. Therefore: Probability (Jack) = 4/52 = .077 Now we can plug these values into our combination formula to get our answer. P (4 or 6, 2 heads, Jack) = P(4 or 6) * P(2 Heads) * P(Jack) P (4 or 6, 2 heads, Jack) = .33 * .25 * .077 = .00635 There is a .635% chance of rolling a 4 or 6, flipping a heads twice, AND drawing a Jack.

theoretical