Question: There’s a popular game called Bunco! It usually involves a group of women getting together, playing a game which requires little or no brain power, and winning some sort of ‘prize’ at the end. I went once (and I will never go again), and won a picnic basket, a beach towel, and a cool water bottle (which I lost within the first week of having it).

In any case, in Bunco you roll 3 dice (they are fair dice, six sides with 1-6 dots), and gain points based on what you roll.

(Note: You may want or need to make a table – you could use excel – to do this problem, it’s not required but is useful if you want to check your answers, or if you’re not confident that you’re doing the calculations correctly.)

Assume it’s the 4^th round, so 4 is the number you want – you get more points that way!

a) What is the probability of getting a BUNCO (on your 1^st roll)? (three of a kind – all 4s)

b) What’s the probability of rolling one four on the first roll and two 4s on the 2nd roll?

c) What’s the probability of getting no points (no fours) on your roll and thus, having to pass the dice to the next person?

d) Challenge (but still required): What’s the probability of winning every round – getting BUNCO on the first roll of every round (3 ones in the first round, then 3 twos in the second round – up to the 6^th round)?