#3
Chapter 13
PROBABILITY
1.
Two cards are drawn successively with replacement from a well-shuffled deck of
52 cards. Find the probability distribution of the number of aces.
2.
Two cards are drawn from a pack of 52 cards one by one with replacement. Find
the probability distribution of number of face card.
3.
A bag contains 1 red and 3 white balls. Find the probability distribution of the
number of red balls if 2 balls are drawn at random from the bag one-by-one
without replacement.
4.
Find the mean of the number obtained on a throw of an unbiased die.
5.
A random variable X has the following probability distribution:
X
0
1
2
3
4
5
6
7
P(X)
0
𝑘
2𝑘
2𝑘
3𝑘
𝑘2
2𝑘 2
7𝑘 2 + 𝑘
Determine
(i) 𝑘
6.
(ii) P(X < 3)
(iii) P(X > 6)
(iv) P(0 < X < 3)
Four bad oranges are mixed accidently with 16 good oranges. Find the probability
distribution of the number of bad oranges in a draw of two oranges.
7.
There are 5 cards numbered 1 to 5, one number on one card. Two cards are
drawn at random without replacement. Let 𝑋 denote the sum of the numbers on
two cards drawn. Find the mean of 𝑋.
8.
Three numbers are selected at random (without replacement) from first six
positive integers. Let X denotes the largest of the three numbers obtained. Find
the probability distribution of X. Also, find the mean of the distribution
9.
The probability distribution of a discrete random variable X is given as under:
𝑋
𝑃(𝑋)
1
1
2
2
4
2A
1
5
3
25
1
10
5A
3A
1
25
1
25
Calculate the value of A if E(X) = 2.94
10.
The random variable 𝑋 can take only values 0,1,2. Given that 𝑃(𝑋 = 0) = 𝑃(𝑋 = 1) =
𝑝 such that 𝐸(𝑋 2 ) = 𝐸(𝑋),then find the value of 𝑝.
1.
2.
3.
4.
1
5. (i) 𝑘 = 10
6.
3
(ii) P(X < 3) = 10
21
6
17
(iii) P(X > 6) = 100
7.
𝟔
8.
9.
3
1
10. 𝑝 = 2
3
(iv) P(0 < X < 3) = 10