Question 969421: A fair sided coin is tossed 5 times
1) How many outcomes in the sample space
2) what is the probability that the third toss is heads given that that the first toss is heads
3) Let A be the event that the first toss is heads and B be the event that the third toss is heads. Are A and B independent, why or why not?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! There are 2 outcomes in the first toss, 4 in the second HH HT TH TT; 8 in the third, 16 in the 4th, and 32 in the 5th. Pascal's Triangle
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
It doesn't show the triangular form formatted here, but notice how the top two add to the bottom one.
There are 32 outcomes, if order matters, which it appears to in this question.
Given that the first toss is heads, the probability the third toss is heads is 50%. They are independent. Whatever happened on the first toss has no effect on the third toss.
Tree diagram hard to make here
HT
HH HT TH TT
HHH HHT HTH HTT THH THT TTH TTT
The first toss is heads (4), and you can see that the third toss is heads 50% of the time.
If independent P(outcome 1)* P(outcome 2)= P (outcome 1 and outcome 2)
P (1st toss is heads)=50% Probability third toss is heads is 50%. The first AND third should be heads 25% of the time. You can see 2 of the 8 above are, so they are independent.
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