Instructions:Illustrates the value of the given random variable and its probability distribution.Refer your solution showing 5 steps.
"Two balls are drawn in succession without replacement from an urn containing 5 orange balls and 6 violet balls.Let V be the random variable representing the number of violet balls.Find the value of the random variable V.
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Given,
5 yellow balls and 6 green balls.
Total=11
Step-by-step explanation:
Vis a random variable So value of V can be 0,1 or 2 as two balls are drawn in succession.
When there is 0 green balls SO both balls are yellow.
P(V=0)=\dfrac{^5C_2}{^{11}C_2}=0.18P (V=0)=11C25C2=0.18
Now If there is one green ball ,This can be done in two ways either green first then yellow or vice versa.
P(Z=1)=\dfrac{5}{11}\times \dfrac{6}{10}+\dfrac{6}{11}\times \dfrac{5}{10}=0.545P(Z=1)=115×106+116×105=0.545
When both balls are green.
P(V=2)=\dfrac{^6C_2}{^{11}C_2}=0.272P(Z=2)=11C26C2=0.272
Equation form of PD is-
P(x)=0.09x^2+0.45x+0.18P(x)=0.09x2+0.45x+0.18
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