b) \(P(happy|agree)=345/379=91\%\)
\( P(happy)=1262/1362=92.7\%\)
The percentages are close together, but independence needs that these percentages need to be equal.So they are not independent.
a) \((0.5)^3=1/8\)
b) \(0.5*0.5*0.5=1/8\)
They are both the same probability.Each time you flip a coin there is a probability of \(1/6\) to roll any number from 1-6, so total probability here \((\frac{1}{6})^5\)
a)Neither fastened is \(1-0.84=0.16\) then for two people, \((0.16)(0.16)=0.0256\)
b)\(1-0.0256=0.9744\)
a) HTHTH HHTTT THHTH HHHTT
b) \(11/20\)