1. Consider the simple random experiment of tossing a fair coin twice. a) b) c)
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1. Consider the simple random experiment of tossing a fair coin twice. a) b) c) What is the sample space for this experiment? Based on your sample space, what is the probability of both tosses landing on heads? Let A be the event of the coin landing on heads for the first toss and B be the event of the coin landing on heads for the second toss. How could we use probability notation to denote the joint probability of both tosses landing on heads? (Note: You are not finding a probability here.) Now use the multiplicative law of probability to find the probability of both tosses landing on heads. Your answers from part b) and part d) should match. This means that events A and B are independent. Explain in your own words why these are independent events. d) e)Explanation / Answer
a). The sample space, S = {HH, HT, TH, TT}
b). Probaility of getting two heads = 1/4 = 0.25
c). A: the coin lands as heads on the first toss,
B: the coin lands as heads on the second toss
therefore, the probability that A happens = P(A)
similarly, the probability that B happens = P(B)
And, the notation for the joint probability is P(AB) or P(A,B)
d). When the coin is tossed for the first time, outcomes could either be a Heads(H) or a Tails(T), therefore the sample space becomes, S = {H, T}
the probability of getting a head = P(A) = 1/2
Now, when the coin is tossed for the second time, the sample space remains the same.
the probability of getting a head on the second toss = P(B) = 1/2
and, using the multiplicative rule, P(AB) = P(A)P(B)=(1/2)(1/2)= 1/4 = 0.25
e). The probabilities in part (b) and (d) are same because A and B are independent events i.e happening of one event does not affect the happening of other event. More precisely, when the coin is tossed for the second time, the result is not based on the result of the first toss, therefore, A and B are independent events and we can use the multipicative rule.
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