Calculating Probability: Coin and Die Tossing Scenarios

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The probability of tossing two heads (P(2heads)) is calculated as 1/2 for the first head and 1/2 for the second head, resulting in a total probability of 1/4. For the second question regarding the probability of rolling an even number, the process involves first getting a tail (1/2 probability) and then rolling an even number on a die, which has a probability of 3/6 or 1/2. Therefore, the combined probability for obtaining an even number is 1/2 multiplied by 1/2, equating to 1/4. Both calculations confirm that the probabilities for the scenarios are indeed correct. Understanding these basic probability principles is essential for solving similar problems.
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A fair coin is tossed. If the upface is a head, the coin is tossed again. If the upface is a tail, then a fair die is tossed.

1. Find P(2heads)
2. Find p(an even number appears)



2. Homework Equations ..none



My attempt at a solution...Probability of getting 1 head is 1/2. So two heads would be 1/2 times 1/2=1/4? And I have no idea for the 2nd question...please help!
 
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Hint: What two things have to happen for an even number to appear? What are their probabilities? So...
 
To get an even number, the upface should be tail (p=1/2) and roll an even number on a fair die (1/6x3even numbers on a die)... 1/2x1/6x3...so is 1/4 correct?
 
Yes.
 

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