In an experiment three fair coins are tossed Obtain the prob

In an experiment three fair coins are tossed. Obtain the probability of the following events:

a. two heads appear or all the tosses are the same?

b. Three heads appear or no tosses are the same

let H denotes the event that head has occurred.

T denotes the event that tail has occurred.

so when three fair coins are tossed the sample space is

S={HHH,HHT,HTH,THH,TTH,THT,HTT,TTT} each sample points having the probability 1/8.

a) P[two heads appear or all the tosses are the same]=P[TTH]+P[THT]+P[HTT]+P[TTT]+P[HHH]=5/8 [answer]

b) the event nos tosses are same is a null event as there are only two outcomes and 3 tosses. so atleast two tosses would be same

so P[three heads appear or no tosses are the same]=P[three heads appear]+P[no tosses are the same]=P[HHH]+0=1/8 [answer]