Rajasthan Board RBSE Class 11 Maths Chapter 14 Probability Ex 14.1
Question 1.
From a cartoon of bulbs, 3 bulbs are drawn randomly. Test each bulb and classified into damage (D) and not damage (N). Find the sample space of this test.
Solution:
After drawing first bulb two results D of will be
After drawning 2nd bulb result
= (D,N) × (D,N)
= {DD, DN, ND, NN}
After drawing 3rd bulb result
= (D, N) × {DD, ND, NN}
= {DDD, DDN, DND, DNN, NDD, NDN, NND, NNN}
Thus sample space
S = {DDD, DDN, DND, DNN, NDD, NDN, NND, NNN}
Question 2.
Four cards are drawn from a desk of cards. What will be the n (E) whereas E is an event to draw 1 king 1 queen 1 fack 1 ace.
Solution:
n(E) = Total ways to get a queen
× Total ways to get a queen
× Total ways to get a fack
× Total ways to get 1 ace
= 4 × 4 × 4 × 4 = 256.
Question 3.
A dice is thrown E is an event to getting 4 on dice and getting even number is event F. Are the events E and F mutually exclusive events ?
Solution:
In throwing a dice, sample space
S = {1, 2, 3, 4, 5, 6}
Then according to question
E = {4}
and F = {2, 4, 6}
Thus E ∩ F = {4} ≠ Φ
Thus E and F are not mutually exclusive events.
Question 4.
Two dice and thrown, then
(i) What is the sample space for pair ?
(ii) What is the sample space for sum of digits appear is 8 ?
Solution:
(i) For pair, sample space.
= {(1,1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
(ii) For sum of digit 8, sample space.
= {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}