Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
(i) It is valid as each p(w1) lies between 0 to 1 and sum of p(w1) = 1
(ii) It is valid as each p(w1) lies between 0 to 1 and sum of p(w1) = 1
(iii) It is not valid as sum of p(w1) = 2.8 ≠1
(iv) It is not valid as p(w7) = 15/14>1
Which is impossible
(i), (ii)
(i) ∵ a die is thrown
Let E be the event of getting prime number
∴ E = {2, 3, 5}
n(E) = 3
(ii) E = {2, 4} ∴ n(E) = 2
(iii) E = {2, 4, 6, 3}
⟹ n(E) = 4
Since a pair of dice have been thrown
∴ Number of elementary events in sample space is 62 = 36
(i) Let E be the event that the sum 8 appear on the faces of dice
∴ E = {(2, 6), (3, 5), (4, 9), (5, 3), (6, 2)}
∴ n(E) = 5
(ii) a doublet
Let E be the event that a doublet appears on the faces of dice
∴ E = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
⟹ n(E) = 6
(iii) a doublet of prime numbers
Let E be the event that a doublet of prime number appear.
∴E = {(2, 2), (3, 3), (5, 5)}
(iv) a doublet of odd numbers
Let E be the event that a doublet of odd numbers appear.
∴E = {(1, 1), (3, 3), (5, 5)}
⟹ n(E) = 3
(v) a sum greater than 9
Let E be the event that a sum greater than appear
∴E = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
∴ n(E) = 6
(vi) an even number on first
Let E be the event that an even number on the first dice appear
Which means any number can be appear on second dice,
∴ n(E) = 18
(vii) an even number on one and a multiple of 3 on the other.
Let E be the event that an even number on one and multiple of 3 on the other appears.
∴ E = {(2,3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2), (3, 4) (3, 6), (6, 2), (6, 4)}
∴ n(E) = 11
be the event that either 9 or 11 as the sum of number appear on the faces of dice.
= {(3, 6), (4, 5), (5, 4), (5, 6), (6, 3), (6, 5)}
(ix) a sum less than 6.
Let E be the event that less than 6 as a sum offer on the faces of dice.
∴ E= {(1,1), (1, 2), (1, 3), (1, 4), (2,1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}
∴ n(E) = 10
(x) a sum less than 7.
Let E be the event that less than 7 as a sum appears on the faces of dice.
n(E) = 15
(xi) a sum more than 7.
Let E be the event that a sum more than 7 appear on the faces of dice.
⟹ n(E) = 15
(xii) neither a doublet nor a total of 10.
Let E be the event that neither a doublet nor a sum of 10 appear on the faces of dice.
be the event that either a doublet or a sum of 10 appear on the faces of dice.
{(1, 1), (2, 2), (3, 3), (4, 6), (5, 5), (6, 4), (6, 6)}
(xiii) odd number on the first and 6 on the second.
Let E be the event that an odd number on the first and 6 on the second appear on the faces of dice.
∴ E = {(1, 6), (3, 6), (5, 6)}
(xiv) a number greater than 4 on each die.
Let E be the event that a number greater than 4 appear on each dice
∴ E = {(5, 5), (5, 6), (6, 5), (6, 6)}
(xv) a total of 9 or 11.
Let E be the event that a total of 9 or 11 appear on faces of dice.
∴ E = {(3, 6), (4, 5), (5, 4), (5, 6), (6, 3), (6, 5)}
(xvi) a total greater than 8.
Let E be the event that sum greater than 8 appear.
∴ E = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
∵ Three dice are thrown
∴ n(S) = 63 = 216
Let E be the event of getting total of if 17 or 18
∴ E = {(6, 6, 5), (6, 5, 6), (5, 6, 6), (6, 6, 6)}
Three coins are tossed
∴ n(S) = 23 = 8
(i) E be the event of getting exactly two heads
∴ E = {HHT, HTH, THH}
∴ n (E) = 3
(ii) E at least two heads (two or 3 heads)
∴ E = {HHH, HHT, THH, HTH}
n(E) = 4
(iii) at least one head and one tail
∴ E = {HTT, THT, TTH, HHT, HTH, THH}
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Chapter 33: Probability – Exercise 33.1...
Chapter 33: Probability – Exercise 33.2...
Chapter 33: Probability – Exercise 33.4...