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QuestionFind the probability of picking a walnut first and an almond second from 13 almonds, 8 walnuts, and 19 peanuts.

Studdy Solution

STEP 1

Assumptions1. The container initially contains13 almonds,8 walnuts, and19 peanuts. . After eating a nut, it is not replaced back into the container.
3. Each nut has an equal chance of being chosen.

STEP 2

First, we need to find the total number of nuts in the container. We can do this by adding the number of almonds, walnuts, and peanuts.
Total nuts=Almonds+Walnuts+PeanutsTotal\, nuts = Almonds + Walnuts + Peanuts

STEP 3

Now, plug in the given values for the number of almonds, walnuts, and peanuts to calculate the total number of nuts.
Total nuts=13+8+19Total\, nuts =13 +8 +19

STEP 4

Calculate the total number of nuts in the container.
Total nuts=13+8+19=40Total\, nuts =13 +8 +19 =40

STEP 5

Now, we need to find the probability of choosing a walnut on the first pick. This is the number of walnuts divided by the total number of nuts.
(Walnut first)=Walnuts/Total nuts(Walnut\, first) = Walnuts / Total\, nuts

STEP 6

Plug in the values for the number of walnuts and the total number of nuts to calculate the probability of choosing a walnut first.
(Walnut first)=8/40(Walnut\, first) =8 /40

STEP 7

implify the probability of choosing a walnut first.
(Walnut first)=/40=0.2(Walnut\, first) = /40 =0.2

STEP 8

After eating a walnut, we need to update the total number of nuts in the container and the number of almonds.
Total nuts=Total nuts−1Total\, nuts = Total\, nuts -1Almonds=Almonds−0Almonds = Almonds -0

STEP 9

Plug in the values to update the total number of nuts and the number of almonds.
Total nuts=40−=39Total\, nuts =40 - =39Almonds=13−=13Almonds =13 - =13

STEP 10

Now, we need to find the probability of choosing an almond on the second pick. This is the number of almonds divided by the new total number of nuts.
(Almond second)=Almonds/Total nuts(Almond\, second) = Almonds / Total\, nuts

STEP 11

Plug in the values for the number of almonds and the new total number of nuts to calculate the probability of choosing an almond second.
(Almond second)=13/39(Almond\, second) =13 /39

STEP 12

implify the probability of choosing an almond second.
(Almond second)=/39≈0.333(Almond\, second) = /39 \approx0.333

STEP 13

The probability of both events happening is the product of their individual probabilities.
(Walnut first and Almond second)=(Walnut first)times(Almond second)(Walnut\, first\, and\, Almond\, second) =(Walnut\, first) \\times(Almond\, second)

STEP 14

Plug in the values for the probability of choosing a walnut first and the probability of choosing an almond second.
(Walnut first and Almond second)=0.2times0.333(Walnut\, first\, and\, Almond\, second) =0.2 \\times0.333

STEP 15

Calculate the probability of choosing a walnut first and an almond second.
(Walnut first and Almond second)=0.2times0.333≈0.067(Walnut\, first\, and\, Almond\, second) =0.2 \\times0.333 \approx0.067The probability that you choose a walnut on your first pick and an almond on your second pick is approximately0.067.

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