1. A coin is tossed six times in succession. What is the probability that
at least one head occurs?
1- P(no head is tossed) = \(1-(\frac{1}{2})^6=1-\frac{1}{64}=\frac{63}{64}\)
exactly three heads occur?
\(\binom{6}{3}*0.5^3*0.5^3=\binom{6}{3}*0.5^6=20*0.015625=0.3125\)
more than four heads occur?
That is 5 heads or 6 heads
\(6*0.5^6+0.5^6 = 0.109375\)
2.Suppose a box1 contains (2 red b***s and 1 white) ball and a second box2 contains (2 red ball and 2 white) b***s. One of the boxes is selected at random and a ball drawn..
What is the probability that the ball is white?
P(box1 and white) + P(box2 and white) = 0.5*(1/3)+0.5*(2/4) = (1/6)+(1/4) = 5/12
What is the probability that the ball is white given it came from the 1st box? = 1/3
.....
