**4. ** Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”, C denote the event” three tails show and D denote the event ‘a head shows on the first coin”. Which events are

(ii) simple?

Sample space when three coins are tossed = [Sample space when a coin is tossed thrice!]
S = {HHH, HHT, HTH, HTT, THH, TTH, THT, TTT}
Now,
A = Event that three heads show up = {HHH}
B = Event that two heads and one tail show up = {HHT, HTH, THH}
C = Event that three tails show up = {TTT}
D = Event that a head shows on the first coin = {HHH, HHT, HTH, HTT}
(ii).If an event X has only one...

**4. ** Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”, C denote the event” three tails show and D denote the event ‘a head shows on the first coin”. Which events are

(i) mutually exclusive?

Sample space when three coins are tossed = [Sample space when a coin is tossed thrice!]
S = {HHH, HHT, HTH, HTT, THH, TTH, THT, TTT}
Now,
A = Event that three heads show up = {HHH}
B = Event that two heads and one tail show up = {HHT, HTH, THH}
C = Event that three tails show up = {TTT}
D = Event that a head shows on the first coin = {HHH, HHT, HTH, HTT}
(i). For two elements X and Y to be...

**3. ** An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

Which pairs of these events are mutually exclusive?

For two elements to be mutually exclusive, there should not be any common element amongst them.
Also, A = {(3,6), (4,5), (5, 4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)}
B = {(1,2), (2,2), (3, 2), (4,2), (5,2), (6,2), (2,1), (2,3), (2,4), (2,5), (2,6)}
C = {(3,6), (6,3), (5, 4), (4,5), (6,6)}
Now, A B = (no common element in A and B)
Hence, A and B are mutually...

**3. ** An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

C: the sum is at least and a multiple of

Sample space when a die is rolled:
S = {1, 2, 3, 4, 5, 6}
Let E = Event of rolling a pair of dice (= Event that a die is rolled twice!) [6x6 = 36 possible outcomes]
E = [ {(x,y): x,y S } ] = {(1,1), (1,2)...(1,6),(2,1).....(6,5),(6,6)}
Now,
C: the sum is at least 7 and a multiple of 3
The sum can only be 9 or 12.
C = [ {(a,b): (a,b) E, a+b>6 & a+b = 3k, k I} ]= {(3,6), (6,3), (5, 4), (4,5), (6,6)}

**3.**** ** An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

B: occurs on either die

Sample space when a die is rolled:
S = {1, 2, 3, 4, 5, 6}
Let E = Event of rolling a pair of dice (= Event that a die is rolled twice!) [6x6 = 36 possible outcomes]
E = [ {(x,y): x,y S } ] = {(1,1), (1,2)...(1,6),(2,1).....(6,5),(6,6)}
Now,
B: 2 occurs on either die
Hence the number 2 can come on first die or second die or on both the die simultaneously.
B = [ {(a,b): (a,b) E, a or b = 2 } ]=...

**3. **** ** An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

A: the sum is greater than

Sample space when a die is rolled:
S = {1, 2, 3, 4, 5, 6}
Let E = Event of rolling a pair of dice (= Event that a die is rolled twice!) [6x6 = 36 possible outcomes]
E = [ {(x,y): x,y S } ] = {(1,1), (1,2)...(1,6),(2,1).....(6,5),(6,6)}
Now,
A : the sum is greater than 8
Possible sum greater than 8 are 9, 10, 11 and 12
A = [ {(a,b): (a,b) E, a+b>8 } ]= {(3,6), (4,5), (5, 4), (6,3), (4,6),...

**2.(vi) ** ** **A die is thrown. Describe the following events:

Also find (i)

F = {3, 4, 5, 6}
F' = {3, 4, 5, 6}' = S - F = {1, 2}

**2.(vi) ** ** ** A die is thrown. Describe the following events:

Also find (h)

**2.(vi) ** ** ** A die is thrown. Describe the following events:

Also find (g)

**2.(vi) ** A die is thrown. Describe the following events:

Also find (f)

**2.(vi) ** ** ** A die is thrown. Describe the following events:

Also find (e)

**2.(vi) ** ** ** A die is thrown. Describe the following events:

(d) Also find

**2.(vi) ** ** ** A die is thrown. Describe the following events:

Also find (c)

**2.(vi) ** ** ** A die is thrown. Describe the following events:

Also find (b) .

**2.(vi) **A die is thrown. Describe the following events:

Also find (a)

**2. ** A die is thrown. Describe the following events:

(vi) F: a number not less than 3

When a die is rolled, the sample space of possible outcomes:
S = {1, 2, 3, 4, 5, 6} or {x : x N, x<7}
Given, F : a number not less than 3
F = {x: x S, x 3 } = {3, 4, 5, 6}

**2. ** A die is thrown. Describe the following events:

(v) E: an even multiple greater than 4

When a die is rolled, the sample space of possible outcomes:
S = {1, 2, 3, 4, 5, 6} or {x : x N, x<7}
Given, E : an even number greater than 4
S1 = Subset of S containing even numbers = {2,4,6}
Therefore , E = {6}

**2.** A die is thrown. Describe the following events:

(iv) D: a number less than 4

When a die is rolled, the sample space of possible outcomes:
S = {1, 2, 3, 4, 5, 6} or {x : x N, x<7}
Given, D : a number less than 4
D = {1, 2, 3}

**2. ** A die is thrown. Describe the following events:

(iii) C: a multiple of 3.

When a die is rolled, the sample space of possible outcomes:
S = {1, 2, 3, 4, 5, 6} or {x : x N, x<7}
Given, C : a multiple of 3
C = {3, 6}

**2. ** A die is thrown. Describe the following events:

(ii) B: a number greater than 7

When a die is rolled, the sample space of possible outcomes:
S = {1, 2, 3, 4, 5, 6} or {x : x N, x<7}
Given, B: a number greater than 7
As no number on the die is greater than 7
B =

Exams

Articles

Questions