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Sagot :
The formula to calculate the simple probability is:
[tex]\text{Probability}=\frac{\text{Numer of favorable cases}}{Total\text{ number of cases}}[/tex]And to calculate the probability of multiple independent events (like in this case the number on the cube and the coin) we have to multiply each probability.
Step 1. Calculate the probability that the number rolled is greater than 4.
For the number to be greater than 4, there are two options: 5 or 6.
So the number of favorable cases is 2.
And the total number of cases in the cube is 6 because of the 6 numbers on the cube.
Thus, the probability that the number rolled is greater than 4 is:
[tex]\frac{2}{6}[/tex]We can simplify this fraction by dividing both numbers by 2:
[tex]\frac{1}{3}[/tex]Step 2. Calculate the probability of getting tails in the coin toss.
In a coin, we have two options for the result: heads or tails.
The number of favorable cases for it to be tails is just 1.
And the total number of cases for the result of the coin is 2.
Using the probability formula, we get the probability of the coin toss being tails:
[tex]\frac{1}{2}[/tex]Step 3. Multiply the two probabilities to get the combined probability.
The probability of the two events happening will be:
[tex]\frac{1}{3}\times\frac{1}{2}[/tex]Here we are multiplying 1/3 which is the probability that the number on the cube is greater than 4, and 1/2 which is the probability of the coin toss being tails.
We use this rule to multiply fractions:
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]And the result is:
[tex]\frac{1}{3}\times\frac{1}{2}=\frac{1\times1}{3\times2}[/tex]Solving the multiplications:
[tex]\frac{1}{3}\times\frac{1}{2}=\frac{1\times1}{3\times2}=\frac{1}{6}[/tex]1/6 is the result.
Answer:
[tex]\frac{1}{6}[/tex]
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