8 For this problem use the sample space of four equally likely out- comes S = {h

Question

8 For this problem use the sample space of four equally likely out- comes S = {hh,ht, th, tt) that arises from regarding the coins as distinguishable (described in Examples 3 and 7 of this chapter). Name and explicitly list the events E: the second toss is heads F: the first toss is heads G: at least one toss is heads Use the conditional probability formula on the formula sheet to compute each answer. First compute any probability you will need by listing the event explicitly and adding the probabilities of the outcomes, eg.' En F = {hh) so P(En F-1/4.

Explanation / Answer

Question 8:

a) Probability that the second toss is a head is computed as:

= number of events when the second toss is a head / total number of outcomes possible

= 2/ 4

= 0.5

Therefore 0.5 is the required probability here.

b) Probability that the second toss is heads given that the first toss is heads

= ( number of ways that first toss and second toss both are heads ) / Number of ways in which first toss is heads

= 1/2

= 0.5

Therefore 0.5 is the required probability here.

c) Probability that second toss is heads given that at least one of the toss is heads

= Number of ways in which second toss is heads / Number of ways in which at least one toss is heads

= 2/ 3

= 0.6667

Therefore 0.6667 is the required probability here.

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