Probability

n = number of trials = 4

r = number of success = 3

P(success) = P(H) = p = 1/2 (in 1 toss of a fair coin)

P(failure) = P(T) = q = 1/2

Use the formula nCr [p^(n-r)](q^r) :

(4C3)[(1/2)^1](1/2)^3

= (4C3)(1/2)^4

= 4 x 1/16

= 4/16

= 1/4

The question is unclear. What do you mean by "almost heads". Please restate the question.

Probability is used in genetics to determine the possibilities of offspring having a particular trait

Probability of not 8 heads = 1- Prob of 8 heads. Prob of 8 heads = 0.5^8 = 0.003906 Prob of not 8 heads= 1- 0.003906 = 0.99604

two events are mutually exclusive if they cannot occur at the same time. The classic example is a coin toss where you have either heads or tails, but there is NO WAY to have heads and tails at the same time. Heads and tails are mutually exclusive.

36 times. But also, you might get the opposite result 36 times.

In the case of dice, greater than three, means 4,5 or 6. So, obviously, three cases out of 36.

In applications such as reciprocal authentication and session key generation the requirement is not so much that the sequence of numbers be statistically random but that

the successive numbers of the sequence are unpredictable.

With true random sequences each number is statistically independent of other numbers in the sequence and therefore unpredictable.

In common usage, unlikely means a low probability of occurrence. But as a term in mathematics, an unlikely event is not rigorously defined as a "low number" is subjective. Certainly, in a comparative sense, i.e. event A is less likely to occur than event B, we can state that the probability of occurrence of A is less than B.

1/6

Sample space for rolling a number greater than 4 is {5,6} so 2 choices in total out of 6

P(>4)=2/6=1/3 is the answer

scientific.

Experimental probability

0.5, 1/2, 50% The probability for heads versus tails does not change based on the amount of times the coin is tossed. It will always be a 50% chance.

If there is only one joker, the odds are 1 in 53. If there are two jokers the odds are 1 in 27.

Well the short answer is that your chances are pretty slim. The long answer:

The total number of 13-card hands is 52-choose-13, which equals 52! / (13! * 39!). Any hand without any pairs must have exactly one of each value from 2 to ace. All there is to choose is the suit of each card, for 413 possible pairless 13-card hands. The probability of choosing one of these hands is the quotient of these two numbers, or 413 * 13! * 39! / 52!, which equals 4194304/39688347475, approximately 0.00010568 or 1 in 9462. Another explanation:

Say the first card in your hand is an ace. For the second card, you have to avoid the other three aces in the deck. There are 51 cards, and 48 of them are OK, so the probability that the second card doesn't pair the first card is 48/51. Suppose your second card was a king. For the third card, you now have to avoid all remaining aces and kings. There are 50 cards left in the deck and you have to dodge six of them. So the probability that the third card doesn't pair either of the first two cards is 44/50. Each time you pick a card, there are three more cards you have to avoid, and one fewer card in the deck. So for the 4th card, you have to avoid 9 cards out of 49, giving a probability of 40/49. This continues until the 13th card, when the probability is 4/40. All these things have to happen one after the other, so you have to multiply the probabilities together:

48/51 x 44/50 x 40/49 x 36/48 x 32/47 x 28/46 x 24/45 x 20/44 x 16/43 x 12/42 x 8/41 x 4/40.

This gives the same probability as above (about 1 in 9462).

(0.5)*(0.5)*(0.5) = 0.125 or 12.5% Please note the following in computing probabilities: Each toss is an independent event, the result of one toss does not affect the outcome of the next. The only outcomes are heads and tails. The probability of either outcome is 0.50 and does not change. Also note that many problems in real life are unlike coin flips, events are dependent on each other, outcomes are numerous, and not easily assigned probabilities. This does not necessarily make calculation of probabilities impossible, only more complicated.

2/6 which is redued to 1/3

5/6

Position or speed

gambling is a good use. It is also used in politics and in predictions in science

First off, how do I calculate the probability that any one event occurs. The answer is equal to: Number of Possible Chances of Success / Total Number of Chances In this case, the number of possible chances of success is one (there is only one 6 of Diamonds in any deck of cards). The total number of chances equal 52 (there are 52 cards to choose from). Therefore the probability of picking a 6 of Diamonds on the first card is 1/52 or .019. In order to calculate the probability that the first card is a 6 of Diamonds AND the second card is a 3 of Hearts, you multiply the two probabilities. Prob. of 1st Card 6D AND 2nd Card 3H = Prob. 1st Card 6D * Prob. 2nd Card 3H We already know the probability of getting a 6 of Diamonds on the first card is 1/52 or .019. To calculate the probability of getting a 3 of Hearts on the second card, it is important to remember that random occurances do not affect the probability of other random occurrances. What I mean is, if I were to draw a 6 of Diamonds from a deck of cards and then replace it, the probability that I would pick a 6 of Diamonds again is the same as it was the first time. Even if I flip a coin 5 times in a row and they all landed on heads, the probability that I would flip another heads is still 50/50. So basically we can ignore what happened on the first draw, and jsut calculate the probability of getting a 3 of Hearts. Again we use our probability formula: Number of Possible Chances of Success / Total Number of Chances In this case, the number of possible chances of success is one (there is only one 3 of Hearts in any deck of cards). The total number of chances equal 52 (THIS ASSUMES THAT WE PUT THE 6 OF DIAMONDS BACK INTO THE DECK AFTER THE FIRST DRAW IF NOT THE NUMBER OF CHANCES IS 51). Therefore the probability of picking a 3 of Hearts on the second card is 1/52 or .019. Multiply the two probabilities together to get the probability of both occurring: 1/52 * 1/52 = 1/2704 = .00037 (or a .037 percent of a chance)

Helps for balance like a kangaroo's tail.

In a standard deck of playing cards, there are 26 red cards.