Question

Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. the store manager assures you that 13 of the 47 boxes on the shelf have the secret decoder ring. the other 34 boxes on the shelf have a different gift inside. if you randomly select two boxes of cereal from the shelf to purchase, what is the probability that both of them have the secret decoder ring?

Answer 1

We know that

[probability that both have the secret decoder ring]=(13/47)*(12/46)
[probability that both have the secret decoder ring]=(156/2162)
[probability that both have the secret decoder ring]=0.0722-------> 7.22%

the answer is 0.0722 (7.22%)

Answer 2

Answer: $\dfrac{169}{2209}$

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 =$p=\dfrac{13}{47}$

Using binomial distribution :-

$P(x)=^nC_xp^x(1-p)^{n-x}$, 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 :-

$P(2)=^2C_2 (\dfrac{13}{47})^2(1-\dfrac{13}{47})^{0}\\\\=(1)(\dfrac{169}{2209})\\\\=\dfrac{169}{2209}$

Hence, the required probability = $\dfrac{169}{2209}$