4. michael has a jar containing is dimes and 20 quarters. He randomly draws 3 coins from the jar one after the other without replacement. What is the probability that the second coin he draws is different from the first and the third.

Step 1 ：Let A be the event that first coin is a dime, B be the event that second coin is different from the first, and C be the event that third coin is the same as the second.

Step 2 ：\(P(B|AC)\) = probability that the second coin is different from the first, given that the first is a dime and the third is the same as the second.

Step 3 ：\(P(B|AC) = \frac{P(ACB)}{P(AC)} = \frac{P(ACB)}{P(A)P(C|A)} \)

Step 4 ：Calculate \(P(A)\) = probability that first coin is a dime = \(\frac{s}{s+t}\)

Step 5 ：Calculate \(P(ACB)\) = probability that the first coin is a dime, second is a quarter, and third is a quarter = \(\frac{s}{s+t} \cdot \frac{t}{s+t-1} \cdot \frac{t-1}{s+t-2} \)

Step 6 ：Calculate \(P(C|A)\) = probability that the third coin is the same as the second given that the first coin is a dime = \(\frac{(t)(t-1)}{(s+t-1)(s+t-2)}\)

Step 7 ：Calculate \(P(B|AC)\) = \(\frac{\frac{s}{s+t}\cdot\frac{t}{s+t-1}\cdot\frac{t-1}{0.0s+b-2}}{\frac{s}{s+t}\cdot\frac{(t)(t-1)}{(s+t-1)(s+t-2)}}\)