A pair of fair dice is thrown 24 times.What is the probability that out of 24 throws atleast one is a double 6

Answer 1

In throwing a pair of dice, there are 36 possible outcomes, of which only one is a double 6. On any given throw then, you have therefore 35 chances out of 36 (35/36) of *not* throwing a double-six.

Throwing the dice 24 times, you have (35/36)^24, or 3,698,954 / 7,272,871 (around 50.86%), so the chances of throwing a double-six is 1-(odds of not throwing one), or

3,573,917 / 7,272,871 (around 49.14%).

Hope that helps.

Answer 2

The probablilty of a 6 on the roll of one of your dice is 1 in 6. The probability of rolling a double six is 1 in 6 on the first and 1 in 6 on the second. The probability of rolling a double 6 on any roll of two dice is 1 in 36.

I won't get into the math of the 24 times, but here is the solution:

1 - (35/36)24 = 0.4914 = 49.14%

Answer 3

"at least one double six" covers a lot of possibilities: one double six, two double sixes, etc, so you don't want to calculate the probability directly.
Let's calculate the probability of what you don't want - no double sixes in 24 throws - and subtract it from 1.

Since there are 36 possible outcomes for a pair of dice (six sides*six sides) and only one double six, the probability that you do NOT get a double six in one throw is 35/36

Since all our throws are independent, for twenty-four throws we would multiply this value together 24 times:
probability of getting no double sixes in 24 throws = (35/36)^24

So our final result is:
probability of getting at least one double six: 1 - (35/36)^24

Answer 4

p(at least 1 double 6 | 12 throws) = 1 - (on double 6 | 12 throws)
= 1 - (35/36)^24 ≈ 0.4914038 = 49.14038%

A little less than half.

Answer 5

A definite...especially if your playing Yatsee

Answer 6

WHY DONT YOU GIVE IT A TRY?