00:01
We have given that 10 dice are rows.
00:03
We are going to let x be the number of aces obtained out of 10 dice rows.
00:08
Now the aces are those spaces with one dot only or one pip.
00:14
Now x will follow the binomial distribution since all the 10 rows are independent of each other.
00:21
And n, the number of trials here is 10.
00:24
In each trial, we take a look at the dice and see whether the ace is obtained or not.
00:32
So all the 10 trials are identical and there are only one of two possible outcomes in each trial, success or failure.
00:43
Success would be in the dice, we get an ace.
00:49
The failure would be we did not get an ace.
00:51
And all the 10 trials are independent of each other, which means each dies.
00:59
Whether we get an ace or not is independent of the rest.
01:02
And probability of success in a single trial, that is p.
01:08
And that is probability of obtaining an ace in a row.
01:13
That will be 1 out of 6 since only one face has a value of 1 pip.
01:22
And this remains constant for all the trials.
01:25
So x follows the binomial distribution where n is 10, p is 1 out of 6.
01:31
Now probability x equals to r where r is the number of aces obtained out of 10 rows.
01:38
And that would be 10 choose r, 1 over 6 to the power r.
01:47
And 1 minus 1 over 6 is 5 over 6 to the power 10 minus r.
01:53
Part a on the 5th, probability of obtaining exactly one ace.
01:57
So we're looking at probability x equals to 1.
02:00
So just sub 1 into the r and we'll get this value which is 0 .3230 4 decimal place.
02:25
Now b want to find probability of obtaining at least one a's so we're looking at probability x greater equals to 1.
02:33
Gonna take 1 minus the complement to this case and there'll be x less than 1 and for x less than 1 there's only one case and that's x equals to zero for x equals to zero just sub 0 into the r get 1 minus 0 .161506 and we'll get this value of 0 .838494 which is 0 .8385 four decimal place c probability of obtaining at most four aces so so we're looking at probability x less than or equals to 4.
03:24
Now, this can be split into a few mutually exclusive cases...