Answer: 2/15
Step-by-step explanation: To find this compound probability, first note that there is no replacement.
The probability of drawing the first white token is 4/10 or 2/5.
The probability of drawing the second token is 3/9 or 1/3 because one white token has already been taken away. Now, multiply 2/5 by 1/3 to get the answer, which is 2/15
The probability of selecting two white tokens without replacement is [tex]\dfrac{2}{15}[/tex].
Given:
The number of white tokens is 4.
The number of blue tokens is 6.
To find:
The probability of selecting two white tokens without replacement.
Explanation:
We know that,
[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
The probability of getting first white token is:
[tex]P_1=\dfrac{4}{4+6}[/tex]
[tex]P_1=\dfrac{4}{10}[/tex]
[tex]P_1=\dfrac{2}{5}[/tex]
Now, the number of remaining tokens is 9 and the number of remaining white tokens is 3. So, the probability of getting second white token is:
[tex]P_2=\dfrac{3}{9}[/tex]
[tex]P_2=\dfrac{1}{3}[/tex]
The probability of selecting two white tokens without replacement is:
[tex]P=P_1\times P_2[/tex]
[tex]P=\dfrac{2}{5}\times \dfrac{1}{3}[/tex]
[tex]P=\dfrac{2}{15}[/tex]
Therefore, the probability of selecting two white tokens without replacement is [tex]\dfrac{2}{15}[/tex].
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