Page 184 - Engineering Mathematics Workbook_Final

Probability & Statistics

120. Six identical fair dice are thrown 123. Seven car accidents occurred in a
independently. Let S denote the week. What is the probability that
number of dice showing even
numbers on their upper faces. Then (i) They all occurred on the same day
the variance of the random variable S (ii) No two accidents occur on the

is _________ same day of week.

1 124. A die is rolled two times. Find the
(a) (b) 1
2 probability that

3 (i) Same face appears
(c) (d) 3
2
(ii) Sum is 10

[MS 2005]
(iii) Sum is greater than 10
121. Let X X 2 ,...........X be the (iv) Sum is neither 8 nor 9
,
21
1
random sample from a distribution
nd
1 21 (v) The 2 toss results in a value that
having variance 5. Let X =  X , is higher than first toss.
i
21 i= 1
21 2 125. Four fair six-sided dice are rolled.
S = (  X − X ) . Then the value of
i= 1 i The probability that the
E(S) = __________.
(i) Sum of the results is 22
(a) 5 (b) 100
(ii) Sum of the results is 21
(c) 0.25 (d) 105
(iii) Sum of the results is 20
122. In three independent throws of a fair

dice. Let X denote the number of 126. A man alternately tosses a coin and
upper faces showing six. Then the throws a die beginning with a coin.
What is the probability that he gets
2
value of (3E − X ) is __________ head before he gets 5 or 6 on the die?

20 2 127. Two cards are drawn at random from
(a) (b)
3 3 a pack of 52 cards. What is the
probability that
5 5
(c) (d) (i) both of them from same suit?
2 12

(ii) both of them from different suit?
[MS 2005]
128. A card is selected at random from a

pack of 52 cards. What is the
probability that it is

182