Question

A child throws 2 fair dice. If the numbers showing are unequal, he adds them together to get his final score on the other hand, if the numbers showing are equal, he throws 2 more dice adds all 4 numbers showing to get his final score. The probability that his final

Answer 1

Answer:

The answer is 148/1296.

Step-by-step explanation:

As we know that first 2 dice can land in 36 ways with equal probability. we also know that in six cases, we have to throw the dice 2 more times but the dice doesn't know that. Therefore all 36 possibilities will be equally likely.  

Following are the possibilities after the first two throws:

4/36 we have a total of 6 without a double and we stop.  

26/36 we don't have a total of 6 or a double and we stop.

6/36 we have a double and must continue. We need to look more carefully.

1/36 we have a double 1, we throw 2 more dice and have a 3/36 chance of getting a total of 6.

1/36 we have double 2, we throw 2 more time and have a 1/36 chance of getting 6.

4/36 we have a double 3 or more, we throw again but we can't get 6.

Thus overall a successful outcome has probability of 4/36+1/36×3/36+1/36×1/36=148/1296.

Answer 2

Answer:

The answer is 148/1296.

Step-by-step explanation:

As we know that first 2 dice can land in 36 ways with equal probability. we also know that in six cases, we have to throw the dice 2 more times but the dice doesn't know that. Therefore all 36 possibilities will be equally likely.  

Following are the possibilities after the first two throws:

4/36 we have a total of 6 without a double and we stop.  

26/36 we don't have a total of 6 or a double and we stop.

6/36 we have a double and must continue. We need to look more carefully.

1/36 we have a double 1, we throw 2 more dice and have a 3/36 chance of getting a total of 6.

1/36 we have double 2, we throw 2 more time and have a 1/36 chance of getting 6.

4/36 we have a double 3 or more, we throw again but we can't get 6.

Thus overall a successful outcome has probability of 4/36+1/36×3/36+1/36×1/36=148/1296.

Step-by-step explanation:

Hope this answer will help you.✌️