抛硬币概率公式
概率是数学的一个分支。概率说明事件发生的可能性。一言以蔽之,它可以称为可能性,即事件发生的可能性。它的值始终介于 0(零)到 1(一)之间。 0 表示不可能的事件,1 表示某个事件。下面提到了事件概率的公式,
事件的概率 P(Event)=(有利结果的数量)/(可能结果的总数)
抛硬币概率
在讨论这个概念之前,首先让我们了解抛硬币时可能出现的结果。抛硬币时只有两种可能的结果。那些是头和尾。因此,根据上述概率公式,抛硬币概率公式为:
Coin Toss Probability Formula = (Number of favorable outcomes)/ (Total number of possible outcomes)
Here, when a single coin is tossed – Total number of possible outcomes = 2
So, simplify above formula for single coin toss as,
Coin Toss Probability Formula for single coin toss = (Number of favorable outcomes)/2
示例问题
问题1:投掷一枚硬币时正面朝上的概率是多少?
解决方案:
Let A be the event of getting head when a coin is tossed.
Number of favorable outcomes – {Head} = 1
As per the coin toss probability formula when a single coin is tossed, the probability of getting head P(A) = Number of favorable outcomes/2
P(A) = 1/2 = 0.5
So there is a 50% chance of getting head when a coin is tossed.
问题 2:抛两枚硬币时至少得到 1 条尾巴的概率是多少。
解决方案:
Let B be the event of getting at least 1 tail when two coins are tossed.
Number of favorable outcomes – {(Head, Tail), (Tail, Head), (Tail, Tail)} = 3
Total possible outcomes – {(Head, Tail), (Tail, Head), (Tail, Tail), (Head, Head)} = 4
As per the coin toss probability formula, Probability of getting atleast 1 tail when 2 coins are tossed P(B) = Number of favorable outcomes/Total number of possible outcomes
P(B) = 3/4 = 0.75
So there are 75% of chances of getting at least 1 tail when two coins are tossed.
问题3:投掷两枚硬币时正面或反面的概率是多少。
解决方案:
Let C be the event of getting head or tail when a coin is tossed.
Number of favorable outcomes – {Head, Tail} = 2
As per the coin toss probability formula when a single coin is tossed, the probability of getting head or tail P(C) = Number of favorable outcomes/2
P(C) = 2/2 = 1
So there is a 100% chance of getting head or tail when a single coin is tossed.
This is an example for sure (or) certain event.
问题4:抛一枚硬币同时出现正面和反面的概率是多少?
解决方案:
Let D be the event of getting head and tail when a coin is tossed.
Here there are no favorable outcomes because when a coin is tossed only 1 possible outcome is obtained either a head or tail but both are not obtained.
Number of favorable outcomes – {} = 0
As per the coin toss probability formula when a single coin is tossed, Probability of getting head and tail P(D)= Number of favorable outcomes/2
P(D) = 0/2 = 0
So there are 0% chances of getting head and tail at the same time when a coin is tossed.
This is an example of an impossible event.
问题 5:当同时抛 3 个硬币时,三个正面都出现的概率是多少?
解决方案:
Let E be the event of getting all three heads when 3 coins are tossed.
When 3 coins are tossed the possible outcomes are ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})
So total number of possible outcomes = 8
The total possible outcomes can also be found by multiplying the number of outcomes of each event together. Here 3 coins are tossed. For each coin toss, there will 2 outcomes. So by multiplying outcomes of each toss i.e., 2 × 2 × 2 = 8 total number of possible outcomes are obtained.
Number of favorable outcomes – {HHH} = 1
As per the coin toss probability formula, Probability of getting all three heads
P(E) = Number of favorable outcomes/Total number of possible outcomes
P(E) = 1/8 = 0.125
So, there is 12.5% chances of getting all 3 heads when 3 coins are tossed.
问题 6:同时抛 3 个硬币时,至少得到两个正面的概率是多少?
解决方案:
Let F be the event of getting atleast two heads when 3 coins are tossed.
When 3 coins are tossed the possible outcomes are ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})
So, the total number of possible outcomes = 8
Number of favorable outcomes – ({HHT}, {HTH}, {THH}, {HHH}) = 4
As per the coin toss probability formula, the Probability of getting at least two heads
P(F)= Number of favorable outcomes/Total number of possible outcomes
P(F) = 4/8 = 1/2 = 0.5
So, there is 50% chance of getting atleast two heads when 3 coins are tossed.