1. ## Basic probability issues!

In a bingo game, balls numbered 1-75 are placed in a bin. Balls are randomly drawn and not repalced. Find each probability for the first 5 balls drawn.
11. P(selection 5 two digit numbers): (22/25)(21/24)(20/23)(19/22)(18/21)=.495 (but this is not what's in the back of the book?)
13. P(5 even numbers or 5 numbers less than 30)...I don't think I'm using the proper logic in finding the probability of even numbers or numbers less than 30. I'm going to omit my work for that reason..

Thanks!

2. Hello, puzzledwithpolynomials!

In a Bingo game, balls numbered 1-75 are placed in a bin.
Balls are randomly drawn and not replaced.
There are: . ${75\choose5} \:=\:17,\!259,\!390$ possible outcomes.

Find each probability for the first 5 balls drawn.

11. P(5 two-digit numbers)
There are 66 two-digit numbers (from 10 to 75).

There are: . ${66\choose5} \:=\:496,496$ ways to get 5 two-digit numbers.

Therefore: . $P(\text{5 two-digit numbers}) \:=\:\frac{496,\!496}{17,\!259,\!390} \;\approx\;0.0288$

13. P(5 even numbers or 5 numbers less than 30)
There are: . $\begin{array}{c}\text{37 even numbers} \\ \text{29 numbers less than 30} \\ \text{14 even numbers less than 30}\end{array}$

Hence, there are: . $37 + 29 - 14 \:=\:52$ numbers which are even or less than 30.

And there are: . ${52\choose5} \:=\:2,598,960$ ways to get a number which is even or less than 30.

Therefore: . $P(\text{even or less than 30}) \;=\;\frac{2,\!598,\!960}{17,\!259,\!309} \;\approx\;0.1506$