Respuesta :
To find the probability of two events happening, we must multiply the probability of each separate event happening by the other.
So, for the first time that you pick a pencil, we have to find the probability that it is a yellow pencil.
Probability = favorable outcomes / total possible outcomes = 7 yellow / 7 yellow + 5 green = 7 yellow pencils / 12 total pencils
Thus, the probability of the first event is 7/12.
According to the question, we want to pick a yellow pencil both times, but we don't replace it. So, assuming we pick a yellow pencil, we have to subtract that from the next calculation.
Thus, probability of the second event = probable outcomes/ total outcomes = 6 yellow pencils / 6 yellow + 5 green pencils = 6 / 11
Therefore, the second event's probability is 6/11.
To find the total probability, we must multiply the two fractions together.
7 / 12 * 6 / 11 = 42 / 132
But, we want to simplify this fraction, so:
42 / 132 = 42 ÷ 6 / 132 ÷ 6 = 7/22
Thus, the probability is 7/22, or approximately 32%.
Hope this helps! :)
So, for the first time that you pick a pencil, we have to find the probability that it is a yellow pencil.
Probability = favorable outcomes / total possible outcomes = 7 yellow / 7 yellow + 5 green = 7 yellow pencils / 12 total pencils
Thus, the probability of the first event is 7/12.
According to the question, we want to pick a yellow pencil both times, but we don't replace it. So, assuming we pick a yellow pencil, we have to subtract that from the next calculation.
Thus, probability of the second event = probable outcomes/ total outcomes = 6 yellow pencils / 6 yellow + 5 green pencils = 6 / 11
Therefore, the second event's probability is 6/11.
To find the total probability, we must multiply the two fractions together.
7 / 12 * 6 / 11 = 42 / 132
But, we want to simplify this fraction, so:
42 / 132 = 42 ÷ 6 / 132 ÷ 6 = 7/22
Thus, the probability is 7/22, or approximately 32%.
Hope this helps! :)
Hello!
A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability they are both yellow?
Data:
total pencils: 12
green pencils: 5
yellow pencils: 7
We can choose two pieces between the twelve, therefore, we have a simple combination:
[tex]C_{12,2} = \dfrac{12!}{2!(12-2)!} = \dfrac{12!}{2!10!} =\dfrac{12*11*\diagup\!\!\!\!\!\!10!}{2!\diagup\!\!\!\!\!\!10!}=\dfrac{132}{2}=\boxed{66\:different\:ways}[/tex]
Now, we choose two among the seven yellow:
[tex]C_{7,2} = \dfrac{7!}{2!(7-2)!} = \dfrac{7!}{2!5!} =\dfrac{7*6*\diagup\!\!\!\!\!5!}{2!\diagup\!\!\!\!\!5!}=\dfrac{42}{2}= \boxed{21\:different\:ways}[/tex]
Therefore, the probability of both being yellow:
[tex]\dfrac{21}{66}\frac{\div3}{\div3}\to\boxed{\boxed{\frac{7}{22}\:different\:ways}}\:\:or\:\:\boxed{\boxed{\approx 32\:\%\:different\:ways}} \end{array}}\qquad\quad\checkmark[/tex]
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I Hope this helps, greetings ... Dexteright02! =)
