Consider the experiment of tossing a fair coin four times Th

Consider the experiment of tossing a fair coin four times. The coin has two possible outcomes, heads or tails.

a. List the sample space for the outcomes that could happen when tossing the coin four times. For example, if all four coin tosses produced heads, then the outcome would be HHHH.

b. If each outcome is equally likely, what is the probability that all four coin tosses result in heads? Notice that the complement of

Solution

1) out comes are {HHHH,HHHT,HHTH,HTHH,THHH,HHTT,HTTH,TTHH,HTTT,TTTH,TTTT,HTHT,THTH,THTT.,THHT,TTHT}

2)P(NO OF ONLY HEADS)=1/16

P(AT LEAST ONE TAIL IS)=1-P(ALL HEADS)=1-1/16=15/16