Final answer:
To win the lottery by betting on numbers 2 and 9, the combined probability is calculated by multiplying the individual probabilities of drawing each number. The probability of drawing number 2 is 1/10, and subsequently drawing number 9 is 1/9, resulting in a combined probability of 1/90.
Step-by-step explanation:
The question asks about the probability of winning a lottery by correctly guessing two specific numbers out of ten. To determine this probability, we must consider the two stages of the lottery separately. Initially, any one of the ten balls can be drawn, so the probability of drawing the first number you bet on, which is 2 in this case, is 1/10. Once the first ball is chosen, it is not replaced, meaning the second selection will be made from the remaining nine balls. Therefore, the probability of drawing the second number you bet on, number 9, after having already drawn number 2, is 1/9. We use the product rule because we need the outcome of drawing both numbers.
Using the product rule, the combined probability of drawing both numbers in the correct order is calculated by multiplying the probabilities of each individual event. Therefore, the combined probability is (1/10) x (1/9), which simplifies to 1/90. This is the probability of winning the lottery by betting on numbers 2 and 9.