91影视

There are $13$ spade cards in a deck. The total number of cards in the deck is $52$

$Probability\left(P\right)=\frac{Numberoffavourable}{Totalnumberofexhaustive}$

The likelihood of the first card being a spade is calculated as follows:

$P\left(Spade\right)=\frac{Numberofspadecards}{Totalnumberofcards}=\frac{13}{52}=0.25$

If the first card is also a spade, the conditional probability of the second card being a spade is:

$$\begin{gathered} P(Secondspade|Firstspade)=\frac{P(SecondspadeAndFirstspade)}{P(Firstspade)} \\ P(Secondspade|Firstspade)=\frac{\frac{13}{52}脳\frac{13}{51}}{\frac{13}{52}}=0.2353 \end{gathered}$$

As a result, the needed probabilities are $0.25$and $0.2353$, respectively.

The probabilities are:

$$\begin{gathered} P(Secondspade|Firstspade)=\frac{P(SecondspadeAndFirstspade)}{P(Firstspade)} \\ P(Secondspade|Firstspade)=\frac{{\displaystyle \frac{13}{52}}脳\frac{13}{51}}{\frac{13}{52}}=0.2353 \end{gathered}$$

$$\begin{gathered} P(Thirdspade|Secondspade)=\frac{P(ThirdspadeAndSecondspade)}{P(Secondspade)} \\ P(Thirdspade|Secondspade)=\frac{{\displaystyle \frac{13}{52}}脳\frac{12}{51}脳{\displaystyle \frac{11}{50}}}{\frac{13}{52}脳\frac{12}{51}}=0.22 \end{gathered}$$

$$\begin{gathered} P(Forthspade|Thirdspade)=\frac{P(ForthspadeAndThirdspade)}{P(Thirdspade} \\ P(Forthspade|Thirdspade)=\frac{{\displaystyle \frac{13}{52}}脳{\displaystyle \frac{12}{51}}脳{\displaystyle \frac{11}{50}}脳{\displaystyle \frac{10}{49}}}{{\displaystyle \frac{13}{52}}脳{\displaystyle \frac{12}{51}}脳{\displaystyle \frac{11}{50}}}=0.2041 \end{gathered}$$

$$\begin{gathered} P(Fifthspade|Forthspade)=\frac{P(ForthspadeAndFifthspade)}{P(Forthspade)} \\ P(Fifthspade|Forthspade)=\frac{{\displaystyle \frac{13}{52}}脳\frac{12}{51}脳{\displaystyle \frac{11}{50}}脳{\displaystyle \frac{10}{49}}}{{\displaystyle \frac{13}{52}}脳{\displaystyle \frac{12}{51}}脳{\displaystyle \frac{11}{50}}脳{\displaystyle \frac{10}{49}}}=0.1875 \end{gathered}$$

$0.22,0.20411$, and $0.1875$ are the probability, respectively.

The following formula can be used to compute the value:

$$\begin{gathered} P\left(Spade\right)=\frac{1}{4}脳\frac{12}{51}脳\frac{11}{50}脳\frac{10}{49}脳\frac{9}{48} \\ P\left(Spade\right)=0.000495 \end{gathered}$$

$0.000495$ is the value.

The likelihood of having a flush can be estimated as follows: $$\begin{gathered} P\left(Flush\right)=P(5spades)+P(5Hearts)+P(5Clubs)+P(5Diamonds) \\ P\left(Flush\right)=\frac{33}{66640}+\frac{33}{66640}+\frac{33}{66640}+\frac{33}{66640}=0.00198 \end{gathered}$$

$0.00198$ is the probability.