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What is the probability of making a 7 in one throw of a pair of dice?

A coin is tossed nine times. What is the total number of possible outcomes of the nine-toss experiment? How many elements are in the subset "6 heads and 3 tails""? What is the probability of getting exactly 6 heads and 3 tails in nine tosses of thus unbiased coin?

In a single throw of a pair of dice, find the probability of obtaining a total of 4 or less.

A card is drawn at random from a deck of cards. Find the probability that at least one of the following three events will occur: Event \(\mathrm{A}\) : a heart is drawn. Event \(B\) : a card which is not a face card is drawn. Event \(C\) : the number of spots (if any) on the drawn card is divisible by \(3 .\)

Find the probability of throwing at least one of the following totals on a single throw of a pair of dice: a total 5, a total of 6 , a total of 7 . Define the events \(A, B\), and \(C\) as follows: Event \(A\) : a total of 5 is thrown, Event B: a total of 6 is thrown, Event C: a total of 7 is thrown.

What is the probability of getting a 5 on each of two successive rolls of a balanced die?

Find the probability that a face card is drawn on the first draw and an ace on the second in two consecutive draws, without replacement, from a standard deck of cards.

A coin is tossed 3 times, and 2 heads and 1 tail fall. What is the probability that the first toss was heads?

A coin is tossed 3 times. Find the probability that all 3 are heads, (a) if it is known that the first is heads, (b) if it is known that the first 2 are heads, (c) if it is known that 2 of them are heads.

A hand of five cards is to be dealt at random and without replacement from an ordinary deck of 52 playing cards. Find the conditional probability of an all spade hand given that there will be at least 4 spades in the hand.