Question

# A coin is tossed three times. An outcome is represented by a string of the sort...

A coin is tossed three times. An outcome is represented by a string of the sort

HTT

(meaning heads on the first toss, followed by two tails).

The

8

outcomes are listed below. Assume that each outcome has the same probability.

(a)Check the outcomes for each of the three events below. Then, enter the probability of each event.

 Outcomes Probability HHH HHT HTH HTT THH THT TTH TTT Event A: Exactly two tosses are heads Event B: Not all tosses are the same Event A and B: Exactly two tosses are heads and not all tosses are the same

(b)Suppose not all tosses are the same. (That is, Event

B

occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event

A

. Then, enter the probability that Event

A

occurs given that Event

B

occurs.

 Outcomes given not all tosses are the same Probability HHT HTH HTT THH THT TTH Event A: Exactly two tosses are heads

(c)Give the following probabilities and select the correct option below.

 PA and BPB = PA|B = PA and BPB ▼? PA|B

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