Kyle and Julie are playing a game where they flip a fair coin four times and try to predict the outcomes. Using the sample space of possible outcomes listed below, answer each of the following questions. What is P(A)P(A)P, left parenthesis, A, right parenthesis, the probability that the first flip is heads? What is P(B)P(B)P, left parenthesis, B, right parenthesis, the probability that the second flip is tails? What is P(A\text{ and }B)P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the first flip is heads and the second flip is tails? Are events AAA and BBB independent?
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Answered by
26
Answer:
P(a) = 1/2
P(b)=1/2
P(a and b) =1/4
A and b are independent
Answered by
5
Given:
A fair coin is flipped four times.
A is the event that a head occurs.
B is the event that a tail occurs.
To Find:
(i) P(A)
(II) P(B)
(iii) P(A∩B)
(iv) Are the events A and B independent.
Solution:
Since the coin is fair, head and tail has equal probability to occur.
Since tossing a coin can give only 2 possible outcomes,
- P(Head) = 1/2
- P(tail) =1/2
Therefore,
(i) P(A) = P( head) = 1/2
(ii) P(B) = P(Tail) = 1/2
Now,
(iii) Probablity for the first flip to be head and second flip to be tails is ,
- P(A∩B) = P(A)P(B) = 1/2 x 1/2 = 1/4
Events A and B are independent since tossing a coin can result either of the two independent of previous outcomes.
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