Question

the probability that a professional baseball player will get a hit is 1/3. calculate the exact probability that he will get at least 3 hits in 5 attempts

Answer 1

at least 3 in 5 attempts means 3 or 4 or 5 and you have to calculate these separately
do you know how to do it?

Answer 2

exactly 5 is easiest, it is \((\frac{1}{3})^5\)

Answer 3

exactly 4 is \(\binom{5}{4}(\frac{1}{3})^4(\frac{2}{3})\)

Answer 4

since \(\binom{5}{4}=5\) this is \(5\times (\frac{1}{3})^4\times (\frac{2}{3})\)

Answer 5

do you know how to compute exactly 3?

Answer 6

is exactly 3 = \[\left(\begin{matrix}40 \\ 243\end{matrix}\right)\]

Answer 7

you should write it as a fraction

\frac{40}{243}

\[\frac{40}{243}\]

Answer 8

hee hee thx, kinda a noob ^^;

Answer 9

exactly 3 is \(\binom{5}{3}(\frac{1}{3})^3(\frac{2}{3})^2\)
yes, it is \(\frac{40}{243}\) add up to get your answer

Answer 10

\[\frac{51}{243}\] hope that's right :3

Answer 11

yep...reduces to \[\frac{17}{81}\]

Answer 12

thanks for the help! :D