从一副 52 张牌中选择国王、王后或红心杰克的概率是多少?
事件 A 的概率通常写为 P(A)。这里,P 代表可能性,A 代表事件。它说明事件即将发生的可能性。事件的概率只能存在于 0 和 1 之间,其中 0 表示事件不会发生,即不可能,1 表示肯定会发生,即确定性。
如果不确定事件的结果,请借助某些结果的概率,以及它们发生的可能性。为了正确理解概率,以抛硬币为例,会有两种可能的结果——正面或反面。
概率公式
Probability of an event, P(A) = Favorable outcomes / Total number of outcomes
从一副牌中随机选择一张牌
众所周知,一副洗好的牌有 52 张牌,因此牌的总数为 52。所有牌进一步分为花色(其中 4 种:黑桃、红心、方块、梅花),每张 13 张牌。
每套花色有 13 张牌(A、2 到 10、Jack、Queen、King)。因此,结果总数将是 52。在 52 个中,King、Queen 和 Jack(或 Knaves)是面卡。在 52 张扑克牌中,总共有 12 张面牌。
使用概率公式,我们可以找到从 52 张牌中随机抽取的牌的概率:
Probability of an event, P(A) = Favorable outcomes / Total number of outcomes.
示例:从 52 张牌中选出第 2 张牌的概率是多少?
解决方案:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
probability of getting 2 = 4
Total number of outcomes = 52
so probability of having number 2 card is = Probability of an event, P(A)
= Favorable outcomes / Total number of outcomes.
= 4/52
= 1/13
从一副 52 张牌中选择国王、王后或红心杰克的概率是多少?
解决方案:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
probability of getting king of heart = 1/13
probability of getting a queen of heart = 1/13
probability of getting a jack of heart = 1/13
Therefore probability of getting a king , queen or jack heart = {probability of getting king of heart + probability of getting a queen of heart + probability of getting a jack of heart}
= 1/13 + 1/13 + 1/13
Probability of getting a king, queen or jack heart = 3/13
类似问题
问题 1:从一副 52 张牌中抽出一张牌时,得到红心或 J 的概率是多少?
解决方案:
It is known that a well-shuffled deck has 52 cards
Total number of black cards = 26
Total number of red cards = 26
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
probability of getting either a heart or a jack?
probability of getting a heart = 13
probability of getting a jack = 4
And probability of getting a jack of heart = 1
Therefore probability of getting a heart = {total number of heart cards in the deck}/{total number of cards in the deck}
= 13/52
Probability of getting a heart = 1/4
And the probability of getting either a jack = {total number of jack cards in the deck}/{total number of cards in the deck}
= 4/52
Probability of getting a jack = 1/13
probability of getting a jack of heart = {total number of jack of heart in the deck}/{total number of cards in the deck}
= 1/52
问题 2:如果你从 52 张牌中随机选择,不选国王的概率是多少?
解决方案:
In one pack of cards there are 4 kings in a deck of 52,
therefore , the probability of drawing a king is = Probability of an event, P(A)
= Favorable outcomes / Total number of outcomes
= 4/52
= 1/13
Hence, the probability of not picking a king P(B) = 1 – P(A)
= 1 – 1/13
= 12/13
Therefore the probability of not picking a king if you choose randomly from a pack of 52 cards is 12/13
问题3:得到国王牌或红牌的概率是多少?
解决方案:
Total number of cards are 52
number of red cards are 26 and kings are 4 whereas 26 red cards contain 2 kings (so only 2 will be considered out of 4).
So, total outcomes = 52
favorable outcomes = 26 + 2 = 28
So, the probability of getting a king or red card = Favorable outcomes / Total outcomes
= 28 / 52 = 7/13
P = 7/13
Therefore the probability of getting a king or a red card is 7/13
问题 4:求一次掷骰子得到小于 3 的数字的概率。
解决方案:
When the dice is rolled then there will be 6 outcomes.
Total number of favorable outcome {set of outcome} = {1, 2, 3, 4, 5, 6}
= 6
Now as per the question,
Probability of getting a number less than 3 in a single throw is 2
Numbers less than 3 are {1,2}
therefore favorable outcome will be = 2
P(A) = Favorable outcomes / Total number of outcomes
= 2/6
= 1/3
Hence the probability of getting a number less than 3 in a single throw of a die is 1/3
问题 5:从一副洗好的 52 张牌中抽出一张牌。求得到黑桃 3 的概率?
解决方案:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
number of favorable outcome of having 3 of spades = 1
therefore the probability of getting 3 of spades = number of favorable outcome / total number of outcome
= 1/52
问题 6:有杰克卡的概率是多少?
解决方案:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
number of favorable outcome of having jack = 4
therefore the probability of having jack card = number of favorable outcome / total number of outcome
= 4/52
= 1/13
问题 7:有 3 颗红心的概率是多少?
解决方案:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
number of favorable outcome of having 3 of heart = 1
therefore the probability of having jack card = number of favorable outcome / total number of outcome
= 1/52
= 1/52