Mathematics Asked by Janine on November 20, 2020
A coin is tossed twice. What’s the probability that exactly 1 head occurs?
A coin is tossed 5 times in succession. What’s the probability that at least 1 head occurs?
On #1, I’m guessing it’s 1/2 because the sample space could be {HH,HT,TH,TT}. Four possibilities in total, two of which have exactly one head occurring.
On #2, I have no idea how to tackle this one, but my assumption is to multiple 1/2 five times.
Any help will do. Thanks in advance.
You're absolutely right on the first question. Each outcome in the sample space is equally likely with probability $.25$. Since we have two outcomes wit one head $2 * .25 = frac{1}{2}$
Now for the second problem. Whenever you see at least we should always think of the rule of complements. So
$$P(text{at least 1 Head}) = 1 - P(text{no heads})$$
Now what is $P(text{no heads})$? Well this is the situation we have 5 Tails $$P(text{no heads}) = P(text{5 Tails}) = (frac{1}{2})^5 = frac{1}{32}$$
Now returning to $P(text{at least 1 Head})$
$$P(text{at least 1 Head}) = 1 - P(text{no heads}) \ = 1 - frac{1}{32} = frac{31}{32}$$
Oh, and of course I am assuming this is a fair coin, otherwise we'd just replace the probability of heads with $p$
Answered by BigBear on November 20, 2020
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