Question

Find the probability distribution of number of heads in three tosses of a coin

Answer 1

your probability is
p3 heads if at least 1 head=Number of cases with 3 headsNumber of cases with at least 1 head
p3 heads if at least 1 head=Number of cases with 3 headsNumber of cases with at least 1 head
However you know that
p3 heads=Number of cases with 3 headsNumber of all cases
p3 heads=Number of cases with 3 headsNumber of all cases
and
pat least 1 head=Number of cases with at least 1 headNumber of all cases
pat least 1 head=Number of cases with at least 1 headNumber of all cases
From this, it is not hard to see that
p3 heads if at least 1 head=p3 headspat least 1 head
p3 heads if at least 1 head=p3 headspat least 1 head
Now you surely know that p3 heads=(12)3=18p3 heads=(12)3=18 and pat least 1 head=1−p3 tails=78pat least 1 head=1−p3 tails=78. Inserting then again gives p3 heads if at least 1 head=18/78=17p3 heads if at least 1 head=18/78=1/7
answer is 1/7 follow me