three unbiased coins are tossed simultaneously.what is probability of getting atmost two heads?

asyoulikeithelp | Student

No.of possible outcomes=8

Possible Outcomes= HHT, HHH, HTH, TTH, TTT, TTH, THT,THH

Atmost two heads means maximum two heads so anything with two heads or less... therefore seven of the possible outcomes have two heads or less. Hence, since no. of possible outcomes is eight and there are seven possibilities with two heads or less the answer is 7/8

neela | Student

 Three unbiased coins are totossed. The situation  is as follows:

No head :      TTT......3C0 = 1 way only  this can happen

one head:     HTT  or THT or TTH  = 3C1 =  one of these 3ways the event  can happen

2heads:        HHT  or HTH or THH = 3C2 =  one of these 3 ways theis event can happen

All 3 heads: HHH onyl 1 way this event,

So in a toss  of 3 unbiased coins, the above one of the 4 types of event can happen in any one of 8 different ways. But getting atmost 2heads is the event of 1st type  or2nd type  or 3rd types  in any one of 1+3+3 = 7 ways.

So probablity getting atmost 2 heads = Pr (0 head or 1 head or 2heads ) = pr(0 head)+Pr(1head)+pr(2H)  1/8+3/8+3/8  = 7/8 .