Question

Consider a bag that contains 218 coins of which 6 are rare Indian pennies. For the given pair of events A and​ B, complete parts​ (a) and​ (b) below. ​A: When one of the 218 coins is randomly​ selected, it is one of the 6 Indian pennies. ​B: When another one of the 218 coins is randomly selected​ (with replacement), it is also one of the 6 Indian pennies.
a. Determine whether events A and B are independent or dependent.
b. Find​ P(A and​ B), the probability that events A and B both occur.

Answer 1

Answer: (a) Independent events , (b) 0.00075

Step-by-step explanation:

Since we have given that

Number of coins = 218

Number of rare Indian pennies = 6

Let Event A: When one of the 218 coins is randomly​ selected, it is one of the 6 Indian pennies.

Event B :  When another one of the 218 coins is randomly selected​ (with replacement), it is also one of the 6 Indian pennies.

As we know that

$P(A)=\dfrac{6}{218}=0.0275\\\\and\\\\P(B)=\dfrac{6}{218}=0.0275$

(a) so, they are independent events as there is a condition of 'with replacement'.

(b) P(A and B) is given by

$P(A\cap B)=P(A).P(B)=0.0275\times 0.0275=0.00075$

Hence, (a) Independent events , (b) 0.00075