Answer:
A= 0.55,B=0.55,C=0.3025,D=0.1664; A and B are independent
Step-by-step explanation:
probability of tail:0.55
probability of not a tail: 0.45
A= P(tail and tail and tail)+P(tail and not tail and tail) + P(tail and not tail and not tail)+P(tail and tail and not tail)
A= 0.55×0.55×0.55+0.55×0.45×0.55+0.55×0.45×0.45+0.55×0.55×0.45
A=0.55
B= P(tail and tail and tail)+P(not tail and tail and tail)+P(tail and tail and not tail)+P(not tail and tail and not tail)
B=0.55×0.55×0.55+0.45×0.55×0.55+0.55×0.55×0.45+0.45×0.55×0.45
B= 0.55
C=P(tail and tail and tail)+P(tail and tail and not tail)
C=0.55×0.55×0.55+0.55×0.55×0.45
C=0.3025
D=P(tail and tail and tail)
D=0.55×0.55×0.55
D=0.1664
For events to be independent, the probability of occurance of one event must not be dependent on the outcome of other event.
Here, first and second flip have to be tail for C and D to happen. However, if first flip is a tail then second slip may or may not be a tail!