Question

A bag contains 3 gold coins and 7 silver coins. The bag contains nothing else. If 3 coins are selected at random and without replacement from the bag, what is the probability that exactly 2 of the coins are silver?

Answer 1

Hi there!
Here's the answer:

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Given,
In a bag,
No. of Gold coins = 3
No. of Silver coins = 7
•°• Total No. of Coins in the bag = 10.

The event is selecting Exactly 2 silver coins from the bag

=> Choose 2 Silver coins First.
=> As per the condition, exactly 2 silver coins is enough. so select 1 more coin from gold


^^^ Here, The total no. of coins that exists after each coin selection has to be considered as the event is considered without Replacement.

• Total No. of coins = 10
¶ No. of ways of selecting 1 silver coin from 7 silver coins
=> 7C1 = 7

• Total No. of coins = 9
¶ No. of ways of selecting 1 more silver coin from 6 silver coins
=> 6C1 = 6

• Total No. of coins = 8
¶ No. of ways of selecting 1 gold coin from 3 gold coins
=> 3C1 = 3


¶¶¶ Required probability
= (7/10) × (6/9) × (3/8)
= (7/40) × 3
= 21 / 40.

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Hope it helps