If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hypergeometric distribution. If a population has \( A \) objects of one type, while the remaining \( B \) objects are, the other type, and if \( n \) objects are sampled without replacement, then the probability of getting \( x \) objects of type \( A \) and \( n-x \) objects of type \( B \) under the hypergeometric distribution given by the following formula. In a lottery game, a bettor selects six numbers from 1 to 51 (without repetition), and a winning six-number combination is later randomly selected. Fin the probabilities of getting exactly two winning numbers with one ticket. (Hint: Use \( A=6, B=45, n=6 \), and \( x=2 \) ) \( P(x)=\frac{A!}{(A-x)!x!} \cdot \frac{B!}{(B-n+x)!(n-x)!} \div \frac{(A+B)!}{(A+B-n)!n!} \) \( P(2)=\square \) (Round to four decimal places as needed)

A six-sided die is rolled. Let A be the event "getting an odd prime number". (1) Write down the set \( \mathrm{A}, \mathrm{n}(\mathrm{A}) \) and \( \mathrm{P}(\mathrm{A}) \). (2) Draw a Venn diagram showing the actual outcomes. (3) Draw a Venn diagram showing the number of outcomes. (4) Draw a Venn diagram showing the probabilities.

9.1 Given: \( P(A)=0,45 ; P(B)=y \) and \( P(A \) or \( B)=0,74 \). Determine the value(s) of \( y \) : 9.1.1 If \( A \) and \( B \) are mutually exclusive events. 9.1.2 If \( A \) and \( B \) are independent events.

En una bolsa hay cuatro tarjetas, con los números \( 1,2,3 \) y 4 respectivamente. Si se sacan dos tarjetas de la bolsa, una tras otra y con reposición, ¿cuál es la probabilidad de que la suma de los números obtenidos sea 7 ? A. \( \frac{1}{4} \) B. \( \frac{7}{16} \) C. \( \frac{1}{16} \)

The probability that it will be suminy tomorrow is \( \frac{2}{9} \), If it is sunny, the probability tha Siya plays rugby is \( \frac{8}{15} \). If it is not sumy, the probability that Stya plays rugby is \( \frac{4}{15} \) 9.2.1 Represent the above information on the tree diagram and indicate all the possible outcomes.

Topic - Probability A restaurant offers a 3 course meal. The entrée may be garlic bread \( (G) \) or chicken soup (S), the a) Draw a tree diagram and list (sample space) all the possible combinations for a 3 course meal.