Question

1)Из колоды в 32 листа подряд вынимают 5 карт. Найти вероятность, что все карты одинаковой(разной) масти?

Answer 1

5/32=0.15 
0.15=15% вероятность что все карты одинаковой или разной масти

Answer 2

5:32=0.15625............

Answer 3

Calculation of Probability

To find the probability that all five cards drawn from a deck of 32 cards are of the same (or different) suit, we need to consider the total number of possible outcomes and the number of favorable outcomes.

1. Total Number of Outcomes: - The total number of ways to draw 5 cards from a deck of 32 cards can be calculated using the combination formula: C(32, 5). - The formula for combinations is: C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. - In this case, n = 32 (number of cards in the deck) and r = 5 (number of cards being drawn). - Therefore, the total number of outcomes is C(32, 5).

2. Number of Favorable Outcomes: - To calculate the number of favorable outcomes, we need to consider two cases: when all the cards are of the same suit and when all the cards are of different suits.

Case 1: All cards of the same suit - There are 4 suits in a deck of cards: hearts, diamonds, clubs, and spades. - If we want all 5 cards to be of the same suit, we need to choose one of the 4 suits and then choose 5 cards from that suit. - The number of ways to choose 1 suit is 4. - The number of ways to choose 5 cards from that suit is C(8, 5) since there are 8 cards of each suit in a deck of 32 cards (8 cards per suit * 4 suits). - Therefore, the number of favorable outcomes for all cards of the same suit is 4 * C(8, 5).

Case 2: All cards of different suits - If we want all 5 cards to be of different suits, we need to choose 5 cards from the 4 suits in the deck. - The number of ways to choose 5 cards from 4 suits is C(4, 5). - Since it is not possible to choose 5 cards from 4 suits, the number of favorable outcomes for all cards of different suits is 0.

3. Calculation of Probability: - The probability of an event is given by the formula: Probability = Number of Favorable Outcomes / Total Number of Outcomes. - Therefore, the probability that all 5 cards drawn from a deck of 32 cards are of the same suit is: (4 * C(8, 5)) / C(32, 5).

Let's calculate the probability using the given formula.