SOLUTION: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 21 of the 42 boxes on the shelf have the secret decod

Question 1182240: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is.
The store manager assures you that 21 of the 42 boxes on the shelf have the secret decoder ring.
The other 21 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 decoder ring?
_______
Round decimal to 4 places
Found 2 solutions by mathmate, ikleyn:
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Given:
21 of 42 boxes have ring.
Once opened, cannot be replaced.
Find probability that two randomly selected boxes both have the ring.

Solution:
probability that the first one is a ring
= 21 out of 42
= 21/42
= 1/2
probability that the second box is a ring
= 20 out of 41
= 20/41

Probability that both of them are rings, we use the multiplication rule to get
P(R,R)
= (1/2) * 20/41
= 10/41
= 0.24390... (approximately)
= 0.2439 (to four decimal places)
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
.

This problem is a TWIN to the problem

https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1182242.html

https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1182242.html

which I solved an hour ago.

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