tuffla2022

STRANGE DICE, DIVISIBLE BY 5

Two fair, six-sided dice are rolled. They are marked so that one die has the numbers 1, 3, 5, 7, 9, 11
and the other has the numbers 2, 4, 6, 8, 10, 12. What is the probability that the sum of the numbers rolled
is divisible by 5? Express your answer as a common fraction.

All possible sums:
 [3, 5, 7, 9, 11, 13, 5, 7, 9, 11, 13, 15, 7, 9, 11, 13, 15, 17, 9, 11, 13, 15, 17, 19, 11, 13, 15, 17, 19, 21, 13, 15, 17, 19, 21, 23] 
I count: 36

All in there that are divisible by 5:
 [5, 5, 15, 15, 15, 15, 15]
I count 7

The probability as a fraction:  \(\frac{7}{36}\)  If Your brain hurts, use python

If we use these numbers, and do the math, then Your problem makes absolutely no sense.

If it is so that 3T + 4C leaves room for 5 more barrels, it seems to make more sense, but even en then

we come up with fractions for C, so I advice You to repost the problem with adjusted numbers.

Original numbers:

Water barrels:just numbers, Trucks: T, Cars: C

67 = 2T + 5C

67 - 5 = 3T + 5C, or 67 = 3T + 5C +5

Setting the first line equal to the second:

2T + 5C = 3T + 5C + 5, we subtract 5C on both sides, eliminiating C, and get

2T = 3T + 5, or T = -5  :: This makes absolutely NO sense.

Put this into the topmost line:

67 = -10 + 5C, 77 = 5C, C = 77/5 :: Also makes NO sense.

Adjusted numbers:

67 = 2T + 5C

67 + 5 = 3T + 5C, or 67 = 3T + 5C -5

2T + 5C = 3T + 5C - 5

2T = 3T - 5, or T = 5

Put into topmost:

67 = 10 + 5C, 5C = 57, and so C = 11 2/5 :: Also makes no sense.

A bit of fractions here. Fine. He saved 4/5, leaving 1/5, then spent 2/3 of that. So what he's left with is 1/3 of 1/5 of the paycheck, or 1/3 x 1/5 = 1/15. This is $2. If 1/15 is $2, then the full paycheck is 15 x $2, or $30.

The goali is the same, whatever team You chose. So we have 10 from 15. \(\binom{15}{10} = 3003\)

Python 3.9 says: 2, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288

But NOT 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144

Python also says \(2^{19} = 524,288\)

q(-1)=3

Already answered by BuilderBoi, further down in the thread.

Nice one, there, BuilderBoi...

This is more like how it should look. Sorry, guys.