I’ve been trying to do this question as part of a practice quiz, but can’t seem to get the right answer. Hopefully someone on here can provide some insight, in the case that I face a similar answer on a real test. Any feedback is appreciated!

We have two loaded dice, dice X and dice Y. Dice X comes up 1 with probability 0.2, 2 with probability 0.4, 3 with probability 0.1, and 4 with probability 0.3. Dice Y comes up 1 with probability 0.1, 2 with probability a, 3 with probability b, and 4 with probability 0.2. The probability b is to be determined. You are not asked to compute the probability a.

We throw both dice. Let A be the event that the number of pins on dice Y is strictly bigger than the number of pins on dice X. We want the probability that event A happens to be equal to 0.42.

Give an integer k as answer so that if we set b = k/100, then event A happens with probability 0.42.