Q. 33 Grandkids Mr. Starnes and his wi... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 5: Q. 33 (page 326)

Grandkids Mr. Starnes and his wife have $6$ grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have $2$ extra tickets to a holiday show, and will randomly select which $2$ grandkids get to see the show with them.
a. Give a probability model for this chance process.
b. Find the probability that at least one of the two girls (Piper and Sedona) get to go to the show.

Short Answer

Expert verified

Part(a) The probability model is $X ~ Bin (6, \frac{1}{6}) P (X = 2) = {}^{6}C_{2} 脳 {(\frac{1}{6})}^{2} 脳 {(1 - \frac{1}{6})}^{6 - 2}$

Part(b) The probability that at least one of the two girls (Piper and Sedona) get to go to the show is $0.6$

Step by step solution

Part(a) Step 1 : Given information

We need to give probability model for this chance process.

Part(a) Step 2 : Simplify

We are given that there are $6$ grandchildrens and $2$ of them are needed to picked.

Let number of grandchildren to be choose is X.

Every children has equal chance to get selected, therefore Probability for everyone is $\frac{1}{6}$

Therefore, the probability model is :

$X ~ Bin (6, \frac{1}{6}) P (X) = {}^{6}C_{x} 脳 {(\frac{1}{6})}^{x} 脳 {(1 - \frac{1}{6})}^{6 - x} P (X = 2) = {}^{6}C_{2} 脳 {(\frac{1}{6})}^{2} 脳 {(1 - \frac{1}{6})}^{6 - 2}$

Part(b) Step 1 : Given information

We need to find probability for at least one of two girls get to go to the show.

Part(b) Step 2 : Simplify

As every children has equal chance to be selected , therefore

$P (at least one of the two girls) = P (one of girls) + P (both girls) P (one of girls) = \frac{{}^{2}C_{1} 脳 {}^{4}C_{1}}{{}^{6}C_{2}} = 0.5333 P (both girls) = \frac{{}^{2}C_{2} 脳 {}^{4}C_{0}}{{}^{6}C_{2}} = 0.0667 P (at least one of the two girls) = 0.5333 + 0.0667 = 0.6$