Question

1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]

Answer 1

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1. @ As its fair coins probability of prob. of a head tail 2 Tree diagram of this experimentin

{xHn}, 326-039 22 M MONDAY O {HHT}, Each branch has probability n H 2 ŞHITY st t toss Ann} (THT} I T N TTH) (TTT?

b Sample space - events of how the 3 tosses can be resulta in, - sample space= {HHH}, {HH T} , {MTH}, {HTT} cor) THA (THT},{TTH), 1113

Probability function: As every event in the sample space is equally likely This means - PCE) = 1 2 VEC (L, 8

A = event that there are there are at least two heads in three tosses os PLA) = P(4*3 vfurutzufT+30&t**}). P[HHH} + P(HHT) + P(ATH) + P(THN) Any = 4. I I 2 8

the three tosses OPCB) = P there are exactly 2 heads in e P ( {MHT} J{UTHUR ET HHB) MIC) 3 (Aus). 3xl 8 PLATB) PLANB) p (B) = 1 PC) P(B) E B CA AnB - B q PLANB)- PCB) Also, when its given B it means it is given that enactly a heads have occurred which event A has occured too. PLAJB) = 1 APC ANB B 348 PO PLA) PLA) 1/2 (Ang) means nu ठि