Answer to Question #313721 in Statistics and Probability for Tok

Question

Four balls are drawn in succession without replacement from an urn containing 8 red balls, 5 green balls. Let T be the random variable representing the number of red balls. Find the values of the random variable T. Complete the table.

Answer 1

T = {0,1,2,3,4}

$P(T=0)={\frac {5 \choose 4} {13 \choose 4}}={\frac 5 {715}}={\frac 1 {143}}$

$P(T=1)={\frac {{5 \choose 3}*{8 \choose 1}} {13 \choose 4}}={\frac {80} {715}}={\frac {16} {143}}$

$P(T=2)={\frac {{5 \choose 2}*{8 \choose 2}} {13 \choose 4}}={\frac {280} {715}}={\frac {56} {143}}$

$P(T=3)={\frac {{5 \choose 1}*{8 \choose 3}} {13 \choose 4}}={\frac {280} {715}}={\frac {56} {143}}$

$P(T=4)={\frac {8 \choose 4} {13 \choose 4}}={\frac {70} {715}}={\frac {14} {143}}$