+91-87964 74404
FlagBACK
Question icon
Algebra

A die is tossed twice. A is the event 'the sumof the two numbers uppermost is greater than 5', B the event 'the sum of the two numbers uppermost is less than 8'. Find the probability of these events:

(a) A

(b) B

(c) AB

(d) A U B

Hence show that P(A U B)=P(A)+P(B)-P(A ^ B).

Are A and B mutually exclusive?

Profile image of Burhan Tayyab
15 Years agoGrade
Answers icon

1 Answer

Profile image of Jitender Singh
11 Years ago
Ans:
Hello Student,
Please find answer to your question below
Let x & y be the random number occuring on die 1st & 2nd time respectively.
1\leq x\leq 6
1\leq y\leq 6
Then for the 1stevent
x + y > 5
Number of possiblity
(1,5), (1,6), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3),(5,4),(5,5), (5,6),(6,1), (6,2), (6,3),(6,4), (6,5), (6,6)
Total possibility = 36
P(A) = \frac{26}{36} = \frac{13}{18}
For the 2ndevent:
x + y > 8
(3,6), (4,5), (4,6), (5,4),(5,5), (5,6), (6,3),(6,4), (6,5), (6,6)
P(B) = \frac{10}{36} = \frac{5}{18}
No they are not mutually exclusive. As you can see there is an intersection b/w events of A & B.

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
1 Answer Available

Last Activity: 3 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 3 Years ago