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The probability of throwing either 7 or 11 with two dice is

A) \( \Large \frac{1}{6} \)
B) \( \Large \frac{2}{9} \)
C) \( \Large \frac{1}{8} \)
D) \( \Large \frac{23}{108} \)

Correct Answer:


B) \( \Large \frac{2}{9} \)

Description for Correct answer:
\( \Large n \left(S\right) \) = 36

Events to get 7 = \( \Large \{ \left(1, 6\right) \left(2, 5\right) \left(3, 4\right) \left(4, 3\right) \left(5, 2\right) \left(6, 1\right) \} \)

\( \Large n \left(E_{1}\right) = 6 \)

\( \Large p \left(E_{1}\right) = \frac{n \left(E_{1}\right) }{n \left(S\right) }=\frac{6}{36} \)

Events to get 11 = \( \Large \{ \left(5, 6\right), \left(6, 5\right) \} \)

\( \Large n \left(E_{2}\right)=\frac{n \left(E_{2}\right) }{n \left(S\right) }=\frac{2}{36} \)

\( \Large P \left(E_{1}E_{2}\right) = P \left(E_{1}\right)+P \left(E_{2}\right) \)

= \( \Large \frac{6}{36}+\frac{2}{36}=\frac{8}{36}=\frac{2}{9} \)

Part of solved Statistics questions and answers : >> Elementary Mathematics >> Statistics

Comments

Similar Questions

1). If A and B are the mutually exclusive events then \( \Large P \left(A\cup B\right) \) will be

A). \( \Large P \left(A\right)+P \left(B\right) \)

B). \( \Large P \left(A\right)+P \left(b\right)+POA\cap B \)

C). \( \Large P \left(a\right)+P \left(B\right)-P \left(A\cup B\right) \)

D). \( \Large P \left(A\right)+P \left(B\right)-P \left(A\cap B\right) \)

2). The sum of deviation taken from Arithmetic mean is

A). 2

B). 0

C). 4

D). 5

3). The arithmetic mean of 21, 30, 33, 64 is

A). 35

B). 28

C). 37

D). 42

4). In a symmetrical distribution

A). Mean > Median > Mode

B). Mean < Median < Mode

C). Mean = Median = Mode

D). Mean > Median < Mode

5). The median of the first 42 natural numbers is

A). 21

B). 21.25

C). 21.5

D). 22

6). The mean and mode of the following set of values are
66, 65, 61, 65, 66 60, 65

A). 62 and 63

B). 63 and 64

C). 64 and 65

D). 62 and 65

7). Which two series of the following 3 series have the same mean
Series 1: 10 10 12 10 9 5 7
Series 2:. 8 5 9 10 12 10 10
Series 3: 9 5 12 9 12 6 10

A). series 1 and series 2

B). series 1 and series 3

C). series 2 and series 3

D). none of these

8). The mode of the following data is 2, 3, 5, 3, 7, 3, 5, 2, 7, 3

A). 5

B). 2

C). 3

D). 7

9). The prices of share during the seven days in a week are as
follows:
Price (in Rs.): 102 96 98 101 104 103 100
The Median value is

A). 104

B). 102

C). 101

D). 100

10). The range of the given 'n' values is

A). \( \Large \frac{1}{2} \) standard deviation

B). Maximum value-Mimmum value

C). Standard deviatlon/mean

D). None of these