Final answer:
The probability of drawing a 2-digit number and then the number 4 from a bag of 30 numbered lottery balls is 7/290.
Step-by-step explanation:
To calculate the probability of drawing a 2-digit number and then the number 4, we will treat each event separately and then use the rule of multiplication for independent events. The probability of drawing a 2-digit number (10 through 30) from 30 balls is 21 out of 30, since there are 21 2-digit numbers in that range. After drawing the first ball and not replacing it, the probability of then drawing the number 4 is now 1 out of 29, because there are now only 29 balls left.
To find the combined probability, we multiply the two probabilities:
- Probability of drawing a 2-digit number: 21/30
- Probability of drawing the number 4 next: 1/29
Combined probability = (21/30) * (1/29) = 21/870, which can be simplified to 7/290.