11 cards marked with the letters from the word MATHEMATICS are placed in a bag. James draws 3 cards at random and with replacement. He scores 1 point for every vowel drawn and 2 points for every consonant drawn. Let X denote James' score. Show that [MATH]P(X\geq 4) = \frac{161}{165}[/MATH].
The above is the problem. I tried doing [MATH]P(X\geq 4) = 1-P(X\leq 3) = 1 - \frac{\binom{4}{3}}{\binom{11}{3}}[/MATH] and got the answer.
Why not [MATH]1-\left(\frac{4}{11}\right)^3[/MATH] ?
The above is the problem. I tried doing [MATH]P(X\geq 4) = 1-P(X\leq 3) = 1 - \frac{\binom{4}{3}}{\binom{11}{3}}[/MATH] and got the answer.
Why not [MATH]1-\left(\frac{4}{11}\right)^3[/MATH] ?
