Probability

We can simplify the question by putting it this way: what is the probability that exactly one out of two coin flips is a head? Our options are HH, HT, TH, TT. Two of these four have exactly one head. So 2/4=.5 is the answer.

The answer depends on how many cards are drawn. If you draw 40 cards, the probability is 0.

The probability of not drawing a spade in a random draw of one card from a standard deck is 39/52 = 3/4.

The simplistic answer is that August will have five Mondays if the month starts on a Saturday, Sunday or Monday. Three days out of the seven so the probability is 3/7 = 0.4286. However, that assumes that any day of the week is equally likely and that is not the case. The impact of leap years and their 2800-year cycle is to increase the probability to 0.43

Yes but it is not possible to attach any interpretation to that. The addition of probabilities makes sense only if they are mutually exclusive outcomes of the same trial. If they are, then their sum cannot be greater than 1.

pr(at most one T) = 1 - pr(not two tails) = 1 - 1/2*1/2 = 1 - 1/4 = 3/4

It is 5/6

It is a certainty. If the die is rolled often enough, the probability that two consecutive rolls show a six is 1.

The probability is 0.0599

One in four.

There are 52 cards in the deck; 13 cards in each of four suits. Spades is one of the four suits, so you have one chance in 4 of picking a spade from a shuffled deck.

The answer depends on the number of sides on the spinner and what numbers are on it.

With a single roll of a fair die, the probability is 1/3.

Landslides

Complementary events are events that are the complete opposite. The compliment of event A is everything that is not event A.

For example, the complementary event of flipping heads on a coin would be flipping tails.

The complementary event of rolling a 1 or a 2 on a six-sided die would be rolling a 3, 4, 5, or 6.

(The probability of A compliment is equal to 1 minus the probability of A.)

The Normal curve is a graph of the probability density function of the standard normal distribution and, as is the case with any continuous random variable (RV), the probability that the RV takes a value in a given range is given by the integral of the function between the two limits. In other words, it is the area under the curve between those two values.

Probability

You can get 8 with (2, 6), (3, 5), (4, 4), (5, 3) or (6, 2), each with a probability of (1/6)*(1/6) = 1/36

The the total probability is 5/36 = 0.1388... recurring.

There are 24 possible outcomes:

January-Heads,

January-Tails,

February-Heads,

February-Tails,

March-Heads,

and so on.

It depends on the events.

The answer is 0.5*(Total number of events - number of events with probability = 0.5)

That is, discount all events such that their probability (and that of their complement) is exactly a half.

Then half the remaining events will have probabilities that are greater than their complement's.

September has 9 letter, of which one appears 3 times.

So the number of distinct permutations is 9!/3! = 120,960

The outcome space.

The probability is 1.

1 - 8/36 = 1 - 2/9 = 7/9

26*25 = 650

If it is a fair spinner, then 3/8