Q3
An ordinary die is rolled twice and the
number of spots on the upper face is observed after each roll. The events A,Band C are defined as
A: The
number of spots showing on the first roll is 3. B: The sum of the number
of spots in the two rolls is 6. C: The sum of the number of spots in the
two rolls is 7. Show that A and B are not independent but that Aand C are independent. Are B and C independent?
Q4
Determine the probability p. or an estimate of
it for each of the following events:
(a) A king, ace, jack of clubs, or
queen of diamonds appears in drawing a single card from a well-shuffled
ordinary deck of cards.
(b) The sum 8 appears in a single
toss of a pair of fair dice.
(c) A nondefective bolt will be found
if out of 600 bolts already examined. 12 were defective.
(d) A 7 or 11 comes up in a single
toss of a pair of fair dice.
(e) At least one head appears in
three tosses of a fair coin.
Q5
A ball is drawn at random from a box containing
10 red, 30 white, 20 blue, and 15 orange marbles. Find the probability that the
ball drawn is (a) orange or red. (b) not red or blue, (c) not blue, (d) white,
and (e) red, white, or blue.