Question 1096145: I need help. Thank you.
A biased coin has a 70 % chance of landing on heads. The coin tossed 3 times in a row. What is probability of "exactly 2 heads given that at least 1 head showing up.
2 heads given is hht, hth, thh, so (0.7*0.7*0.3)*3=0.441.
But confused with at least 1 head part.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
Using the format for displaying results that you show in your message....
3 heads is hhh, so (0.7*0.7*0.7) = 0.343.
2 heads given is hht, hth, thh, so (0.7*0.7*0.3)*3=0.441.
1 heads is htt, tht, tth, so (0.7*0.3*0.3)*3 = 0.189.
0 heads is ttt, so (0.3*0.3*0.3) = 0.027.
Note that finding the probabilities of all possible cases can be good practice for a beginning student; it also gives confidence in your method and your calculations to see that the sum of the probabilities for all the cases is 1.
Now.... Since the probability of no heads is 0.027, the probability of at least one head is 1-0.027 = 0.973.
And when the probability question asks for the probability of getting 2 heads, GIVEN THAT THERE WAS AT LEAST 1 HEAD, it means that the sample space is only the outcomes that had at least one head; and that means the denominator of your probability fraction is the probability that there is at least one head.
And finally, since the numerator is the probability of getting 2 heads, the probability fraction for the question that is being asked is 
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