An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
A current of 15.0 A over 30 seconds delivers approximately 450 coulombs of charge. This charge represents approximately 2.81 × 1 0 21 electrons flowing through the device. Thus, this is the number of electrons that flow during that time period.
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Calculate the probability of each outcome.
Compare the probabilities to identify the lowest ones.
Select the three outcomes with the lowest probabilities.
The outcomes are rolling a sum of 6, rolling a sum of 2 or a sum of 9, and rolling a sum greater than 2 but less than 5. ro ll in g a s u m o f 6 , ro ll in g a s u m o f 2 or a s u m o f 9 , ro ll in g a s u m g re a t er t han 2 b u t l ess t han 5
Explanation
Analyze the problem We are given a table representing the possible outcomes of rolling two number cubes. The goal is to identify three outcomes for Marta that have a lower probability of occurring than other outcomes, so that Marta has a lower probability of winning than Elena.
Calculate the probabilities First, we need to calculate the probabilities of each outcome:
Probability of rolling a sum of 7: 36 6 = 6 1 ≈ 0.1667
Probability of rolling a sum of 6: 36 5 ≈ 0.1389
Probability of rolling a sum of 2 or a sum of 9: 36 1 + 36 4 = 36 5 ≈ 0.1389
Probability of rolling a sum greater than 9: 36 6 = 6 1 ≈ 0.1667 (sums of 10, 11, and 12)
Probability of rolling a sum greater than 2 but less than 5: 36 6 = 6 1 ≈ 0.1667 (sums of 3 and 4)
Compare the probabilities Comparing the probabilities, we want to select the three outcomes with the lowest probabilities. From the calculations above, we see that:
Rolling a sum of 6 has a probability of approximately 0.1389.
Rolling a sum of 2 or a sum of 9 has a probability of approximately 0.1389.
Rolling a sum greater than 2 but less than 5 has a probability of approximately 0.1667.
Select the three outcomes Since we need to select three options, and we are looking for outcomes where Marta has a lower probability of winning, we should select the outcomes with the lowest probabilities. The three options with the lowest probabilities are:
rolling a sum of 6
rolling a sum of 2 or a sum of 9
rolling a sum greater than 2 but less than 5
Final Answer The three outcomes that give Marta a lower probability of winning are rolling a sum of 6, rolling a sum of 2 or a sum of 9, and rolling a sum greater than 2 but less than 5.
Examples
This problem demonstrates how probability can be used to analyze games of chance. By calculating the probabilities of different outcomes, we can determine which outcomes are more or less likely to occur. This can be useful in designing games that are fair and balanced, or in developing strategies for playing games that maximize our chances of winning. For example, in a board game, understanding the probabilities of rolling different numbers on a die can help us make informed decisions about which moves to make. Similarly, in a card game, knowing the probabilities of drawing different cards can help us decide when to bet and when to fold. The probabilities were calculated as follows:
P ( s u m = 7 ) = 36 6 P ( s u m = 6 ) = 36 5 P ( s u m = 2 or s u m = 9 ) = 36 1 + 36 4 = 36 5 9) = \frac{6}{36}"> P ( s u m > 9 ) = 36 6 P ( 2 < s u m < 5 ) = 36 6
