An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The total charge delivered by the current over 30 seconds is 450 coulombs. This corresponds to approximately 2.81 x 10^21 electrons flowing through the device. Therefore, the device allows a significant number of electrons to pass through it in that time period.
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Calculate the expected value of playing 'evens': E ( e v e n s ) = 3.5 .
Calculate the expected value of playing 'odds': E ( o dd s ) = 3.5 .
Compare the expected values: E ( e v e n s ) = E ( o dd s ) .
Since the expected values are equal, it does not matter which option Jessica chooses: E ( e v e n s ) = E ( o dd s ) .
Explanation
Analyze the game Let's analyze the game 'Sums' to determine the best strategy. The game involves rolling two dice and summing the results. If the sum is odd, the 'odds' player gets points equal to the sum. If the sum is even, the 'evens' player gets points equal to the sum. We need to calculate the expected value for both 'odds' and 'evens' to determine which strategy is better.
Calculate E(evens) To calculate the expected value for 'evens', we multiply each even sum by its probability and add them up: E ( e v e n s ) = ( 2 × 36 1 ) + ( 4 × 36 3 ) + ( 6 × 36 5 ) + ( 8 × 36 5 ) + ( 10 × 36 3 ) + ( 12 × 36 1 ) E ( e v e n s ) = 36 2 + 36 12 + 36 30 + 36 40 + 36 30 + 36 12 = 36 126 = 3.5 So, the expected value for 'evens' is 3.5.
Calculate E(odds) To calculate the expected value for 'odds', we multiply each odd sum by its probability and add them up: E ( o dd s ) = ( 3 × 36 2 ) + ( 5 × 36 4 ) + ( 7 × 36 6 ) + ( 9 × 36 4 ) + ( 11 × 36 2 ) E ( o dd s ) = 36 6 + 36 20 + 36 42 + 36 36 + 36 22 = 36 126 = 3.5 So, the expected value for 'odds' is 3.5.
Compare E(odds) and E(evens) Comparing the expected values, we find that: E ( e v e n s ) = 3.5 E ( o dd s ) = 3.5 Since the expected values are equal, it doesn't matter whether Jessica chooses 'odds' or 'evens'. The statement that E ( e v e n s ) will be more because there are more even numbers is incorrect.
Final Answer The expected values for both playing odds and playing evens are the same. Therefore, it does not matter which one Jessica chooses to play.
Examples
This type of probability calculation can be used in many real-world scenarios, such as determining the expected return on investment for different financial assets or evaluating the fairness of a game of chance. By calculating the expected value of different outcomes, individuals and organizations can make more informed decisions about which risks to take.
