jar contains colored stones that are 4 pink stones, 9 orange stones and 5 green stones. Ryan picks one stone, records its color and puts it back in the jar. Then he draws another stone. What is the probability of taking out an orange stone followed by the green stone?

Question

27-04-2016
Mathematics

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jar contains colored stones that are 4 pink stones, 9 orange stones and 5 green stones. Ryan picks one stone, records its color and puts it back in the jar. Then he draws another stone. What is the probability of taking out an orange stone followed by the green stone?

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twvogels twvogels · Answer 1 · 2016-04-27T19:15:20+02:00

The probability of two independant events [tex]a[/tex] and [tex]b[/tex] can be found by multiplying the individual probabilities like so: [tex]P_{total} = P_a * P_b[/tex]

For each individual probability we can find the answer via a simplfied representation:
[tex]P_x=\frac{desired}{total}[/tex]

For the first stone (orange) we have:
[tex]P_{orange}=\frac{orange}{total}=\frac{9}{18}=\frac{1}{2}[/tex]

For the second stone (green) we have:
[tex]P_{green}=\fracgreen}{total}=\frac{5}{18}[/tex]
**(Notice that the total is still 18 since he put the first one back in the jar before drawing the second.)

So:
[tex]P_{total}=P_{orange} \times P_{green}[/tex]
[tex]P_{total}=\frac{1}{2} \times \frac{5}{18}[/tex]
[tex]P_{total}=\frac{5}{36} \approx 13.88\%[/tex]