For problem 2a., can you explain to me how they got to the answer? Also how to intuitively approach this problem?

2 Probability WarmUp (3) Suppose that we have a bucket of 30 red balls and 70 blue balls. If we pick 20 balls out of the bucket, what is the probability of getting exactly it red balls (assuming 0 5 k g 20) if the sampling is done with replacement? (b) Same as part (a), but the sampling is without replacement. (c) [f we roll a regular, t'rsided die 5 times. What is the probability that at least one value is observed more than once? Solution: (a) Since there is replacement, each time we sample, the probability of choosing a red ball is 30 f 100. We repeat this sampling independently 20 times. So 20 1m red balls) = ( k )(osfmank. (i \\ I . J 1 .1 . .I' .." .i i 1 1 11 1.1! . .i . .1 ' 1'\"! 1