Question

(binominal experiments and simulations) six coins are tossed. what is the probability that the following occurs? 3. 2 heads or 5 tails

Answer 1

err, what is the "3." is that just the question?

Answer 2

Just a question

Answer 3

so: 2 heads or 5 tails?

Answer 4

Yes..

Answer 5

2 heads

Answer 6

Let \(A:=\{2\:heads\}\), \(B:=\{5\:tails\}\). The number of coins is 6, so the sum of heads and tails is 6. That's why we can say that
\(A=\{2\:heads\:and\:4\:tails\}\)
\(B=\{1\:head\:and\:5\:tails\}\)
Since \(A\cap B=\varnothing\), you have \(P(A\cup B)=P(A) + P(B)\), and
\(P(A) = \binom{6}{2} (\frac12)^{2}(1-\frac12)^{4}\)
\(P(B) = \binom{6}{2} (\frac12)^{1} (1-\frac12)^{5}\)