Answer: [tex]\dfrac{169}{2209}[/tex]
Step-by-step explanation:
Given : The store manager assures you that 13 of the 47 boxes on the shelf have the secret decoder ring.
Then, the probability of getting a box contains secret decoder ring =[tex]p=\dfrac{13}{47}[/tex]
Using binomial distribution :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], P(x) is probability of getting success in x trials, p is probability of getting success in each trial and n is the sample size.
If you randomly select two boxes of cereal from the shelf to purchase, then n=2
The probability that both of them have the secret decoder ring :-
[tex]P(2)=^2C_2 (\dfrac{13}{47})^2(1-\dfrac{13}{47})^{0}\\\\=(1)(\dfrac{169}{2209})\\\\=\dfrac{169}{2209}[/tex]
Hence, the required probability = [tex]\dfrac{169}{2209}[/tex]
