Answer:
a. The two events are dependent.
b. [tex]P(A\cap B)[/tex]= [tex]\frac{1}{220}[/tex].
Step-by-step explanation:
Given
Total coins =220
Number of Indian pennies= 6
A: When one of the 220 coins is randomly selected, it is one of the Indian pennies.
Therefore , the probability of getting an  Indian pennies=[tex]\frac{6}{220 }[/tex]
By using formula of probability=[tex]\frac{Number \; of\; favourable\; cases}{total\; number \; of \;cases}[/tex]
Probability of getting an  Indian pennies=[tex]\frac{3}{110}[/tex]
B: When another one of the 220 coins is randomly selected( with replacement) , It is also one of the Indian pennies.
Therefore, probability of getting an Indian pennies=[tex]\frac{6}{220}[/tex]
Probability of getting an Indian pennies =[tex]\frac{3}{110}[/tex]
[tex]A\cap B[/tex]: 1
[tex]P(A\cap B)=\frac{1}{220}[/tex]
If two events are independent. Then
[tex]P(A\cap B)= P(A)\times p(B)[/tex]
P(A).P(B)= [tex]\frac{3}{110} \times \frac{3}{110}[/tex]=[tex]\frac{9}{12100}[/tex]
Hence, [tex]P(A\cap B)\neq P(A).P(B)[/tex]
Therefore, the two events are dependent.
b. Probability that events A and B both occur
Number of favourable cases when both events A and B occur=1
Total coins=220
Probability=[tex]\frac{Number \; of\; favourable \; cases}{Total\; number\; of\; cases}[/tex]
[tex]P(A\cap B)=\frac{1}{220}[/tex]
