Practicing Success
Three numbers are chosen at random with out replacement from the set of integers {1, 2, 3, ……, 10}. The probability that the minimum of the chosen numbers is 3 or the maximum of the chosen numbers is 7, is equal to |
$\frac{23}{120}$ $\frac{13}{120}$ $\frac{13}{60}$ $\frac{11}{40}$ |
$\frac{11}{40}$ |
Let A : Minimum of the chosen number is 3 B : Maximum of the chosen number is 7 $P(A)=\frac{{ }^7 C_2}{{ }^{10} C_3}=\frac{21}{120}$ $P(B)=\frac{{ }^6 C_2}{{ }^{10} C_3}=\frac{15}{120}$ $P(A \cap B)=\frac{{ }^3 C_1}{{ }^{10} C_3}=\frac{3}{120}$ Thus, required probability $=P(A)+P(B)-P(A \cap B)$ $=\frac{11}{40}$ |