Download Discrete prob probs

1.
A discrete random variable X has the following probability distribution:
x
0
1
2
3
Find
2.
P( X  x )
p
2p
1-2p2
2p-3p2
(a) the value of p;
(b) P( X  2) ;
(c) P( X  2) ;
(d) P( X  2 X  2) .
Urn A contains 5 red and 3 blue marbles; urn B contains 2 red and 4 blue marbles. A marble
is selected from each urn and the colour noted. Let X represent the number of red marbles
selected. Tabulate the probability distribution for X.
3.
A die is tossed 7 times in succession. Find the probability that (a) exactly 2 tosses resulted
in a 6; (b) at least 2 tosses resulted in a 6.
4.
A doctor estimates that his treatment of a particular illness is successful 75% of the time.
Find the probability that he will successfully treat exactly 5 of 6 patients who seek his help.
5.
How many throws of two dice are required to ensure that the probability of obtaining at
least one “double six” is greater than 0.95? (note there are two ways to do this…using the
equation above will yield a situation that requires you to guess and check. You can also try
1  P(no double 6 in n trials) )
6.
Five percent of a large consignment of fruit is inedible. Find the probability that in a
random selection of 10 pieces of fruit from this consignment, exactly two pieces are
inedible. (note: this is not really independent events but the difference will be negligible for
very large consignments)
7.
Three coins are tossed. Let the random variable X represent the number of heads obtained.
Construct a table to represent this probability distribution.
8.
A manufacturer finds that 30% of the items produced from one of the assembly lines are
defective. During a floor inspection, the manufacturer selects 6 items from this assembly
line. Find the probability that the manufacturer finds (a) two defectives (b) at least two
defectives.
9.
Consider the following probability distribution.
x
2
3
4
P(X=x)
0.3
0.5
0.2
Find (i) the mean, (ii) the variance and (iii) the standard deviation.
10. A die is tossed 180 times. Find the mean and standard deviation of the random variable
representing the total number of sixes obtained.
11.
12.
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