Question

A dealer has a stock of 15 gold coins out of which 6 are counterfeits. A person randomly picks 4 of the 15 gold coins. What is the probability that all the coins picked will be counterfeits?​

Answer 1

Answer:

Let E

1

and E

2

be the events that the boxes I and II are chosen respectively.

⟹P(E

1

)=

2

1

=P(E

2

)

Let A be the event that the coin drawn is of gold.

⟹P(A∣E

1

)=P(a gold coin from box I)=

2

2

=1

P(A∣E

2

)=P(a gold coin from box II)=

2

1

Probability that the other coin in the box is of gold = The probability that the gold coin is drawn from box I=P(E

1

∣A)

By using Bayes' theorem,

P(E

1

∣A)=

P(E

1

)P(A∣E

1

)+P(E

2

)P(A∣E

2

)

P(E

1

)P(A∣E

1

)

=

2

1

×1+

2

1

×

2

1

2

1

×1

=

3

2

Hence, P(A∣E

1

)=

3

2