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.

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Respuesta :

windyyork windyyork · Answer 1 · 2019-10-10T07:14:18+02:00

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

[tex]P(A)=\dfrac{6}{218}=0.0275\\\\and\\\\P(B)=\dfrac{6}{218}=0.0275[/tex]

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

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

[tex]P(A\cap B)=P(A).P(B)=0.0275\times 0.0275=0.00075[/tex]

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