I12-03

Question

Daniel is playing a game with a dice and a coin to win up to two prizes.
 
The dice is numbered 1 through 6, and the coin has numbers 1 and 2. Daniel rolls the dice once and flips the coin once.
 
• If the product of the two numbers is even, he wins a smartwatch.
 
• If the dice and coin show the same number, he wins a laptop.
 
Select for  None  the probability that Daniel will not win any prize and for  Both prizes , the probability that Daniel will win both prizes. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

For Daniel not to win any prize, he must: 1. Roll an odd number and get an odd number on the coin flip, as this is the only way to avoid an even product, and 2. Avoid the (1, 1) case (because in this case, the dice and coin show the same number, and he would win a laptop). Therefore, he must roll 3 or 5 on the die and get 1 on the coin flip. The probability of this is (2/6) * (1/2) = 1/6.
 
For Daniel to win both prizes, he must get an even product and matching numbers. This is possible if he rolls 2 and flips 2. The probability of this is (1/6) * (1/2) = 1/12.

Correct answer:

None  "1/6"

Both Prizes  "1/12"

ShilpiAgnihotrii · Answer

that was a great question and good explanation !

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

dnguyen1203 · Answer

I think this is a  high-quality  question and I agree with explanation.

Puneet11 · Answer

I did not quite understand the solution. it should be clearly brought out in problem that the winning and loosing has to be a calculated with a single roll and toss of coin.

Bunuel · Answer

Your doubt is completely unfounded. The problem explicitly states that Daniel "rolls the dice once and flips the coin once." This makes it clear that both winning and losing conditions are determined from a single roll and a single flip, there is no ambiguity. The solution correctly follows this interpretation as given in the problem.

Dereno · Answer

Nice conceptual question

heyRaj · Answer