Question

(I need help, this is three parts :p)
While Playing Yahtzee and rolling 5 dice, Mei gets the result shown at right (the numbers are 2, 4, 4, 4, and 1). Mei decides to keep the three fours and reroll the other 2 dice.
a. what is the probability that Mei will have 5 of a kind?
b. What is the probability that she will have 4 of a kind?
c. what is the probability that she will have exactly three 4's?

Answer 1

The easiest way to do this question is to ignore the dice that have already been rolled. And instead consider them as just two dice.

a. what is the probability Mei will roll 2 fours
b. what is the probability Mei will roll 1 four
c. what is the probability Mei will roll no fours

Answer 2

Would you be able to work that out?

Answer 3

a. 1/6 times 1/6 times
b. 1/6
c. 0

Answer 4

a. 1/6 times 1/6

Answer 5

I think maybe...@riccyscaduto
a. 1/6
b.
c. 5/6

Answer 6

That's close, but you need to consider 2 dice.

So, the probability of rolling a 4 on a single dice would be 1/6

When there are two or more occurrences you need to multiply the probabilities

Answer 7

1/6 chance of rolling a four on the first and 1/6 chance of rolling a four on the second would be?

Answer 8

yeah but if we figure out rolling a four on 2 isn't it 2/12? that simplifies to 1/6....

Answer 9

a. 1/36
b. 1/6
c. 0

Answer 10

You add probabilities when there are more than one way of reaching the same outcome. For this you need to multiply\[\frac{ 1 }{ 6 } * \frac{ 1 }{ 6 }\]

Answer 11

oh yeah
so that would be 1/36

Answer 12

Yeah, that's right.
b. is marginally more complicated. There are two ways of rolling 1 four.

rolling a 1/2/3/5/6 with the first dice and rolling a 4 on the second
or rolling a 4 on the first dice and rolling 1/2/3/5/6 on the second

Answer 13

so \[\frac{ 5 }{ 6 } * \frac{ 1 }{ 6 } \] and\[\frac{ 1 }{ 6 } * \frac{ 5 }{ 6 } \]

Answer 14

Does that make sense? I know it's a little messy

Answer 15

wait so its 5/36?

Answer 16

for one of them, yes and this is what I mentioned earlier, when there are two ways of getting the same outcome you and them so \[\frac{ 5 }{ 36 } + \frac{ 5 }{ 36 }\]

Answer 17

you add them*

Answer 18

so it would be 10/36 or 5/18?

Answer 19

Yes

Answer 20

C is similar to a except it's the chance of not rolling a 4

Answer 21

and the answer to c is the same though

Answer 22

the chance of not rolling a 4 on each dice is 5/6 so the answer would be \[\frac{ 5 }{ 6 } * \frac{ 5 }{ 6 }\]

Answer 23

so 25/36
and it can't be reduced.

Answer 24

yes, so that's all 3 answers

Answer 25

thank you so much!