91影视

Fiver numbers are to be selected from 1 to 33.

One each from picture cards and suit cards is to be selected from four.

The probability of an event is defined as:

$P\left(A\right)=\frac{\text{Number}\text{of}\text{favorable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Favorable outcomes would support the occurrence of event A out of the total number of outcomes.

Combination is the measure to compute the number of ways to pick a certain number of items from a set of values.

The formula to select r items from n using the combination rule is:

${}^n{C}_r=\frac{n!}{\left(n-r\right)!脳r!}$

a.

The number of ways in which five numbers can be chosen from 1 to 33 is:

$$\begin{gathered} {}^{33}{C}_5=\frac{33!}{\left(33-5\right)!脳5!} \\ =237336 \end{gathered}$$

Thus, the number of ways to pick five number cards from 1 to 33 is 237336.

The number of correct combinations is 1.

The probability of event E, i.e., selecting the correct five numbers from 1 to 33 is:

$P\left(E\right)=\frac{1}{237336}$

Thus, the probability of selecting the correct five numbers is $\frac{1}{237336}$ .

b.

The number of cards that is correct is 1.

The total number of picture cards is 4.

The probability of event F, i.e., selecting the correct picture card is:

$P\left(F\right)=\frac{1}{4}$

Thus, the probability of selecting the correct picture card is $\frac{1}{4}$.

c.

The number of suit cards that are correct is 1.

The total number of suit cards is 4.

The probability of event G, i.e., selecting the correct suit card is:

$P\left(G\right)=\frac{1}{4}$

Thus, the probability of selecting the correct suit card is $\frac{1}{4}$.

d.

When multiple events occur together, the probability of co-occurrence is computed as the product of all these events. This is stated as the multiplication rule.

The probability of selecting a five number card, picture card, and suit card is computed as follows:

$$\begin{gathered} P\left(E\text{and}F\text{and}G\right)=P\left(E\right)脳P\left(F\right)脳P\left(G\right) \\ =\frac{1}{237336}脳\frac{1}{4}脳\frac{1}{4} \\ =\frac{1}{3797376} \end{gathered}$$

Thus, the probability of selecting a five number card, picture card, and suit card is $\frac{1}{3797376}$.