Question 31 (A) - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards
Last updated at Sept. 29, 2024 by Teachoo
Question 31 (A) – (
i
)
The probability that it rains today is 0.4 . If it rains today, the probability that it will rain tomorrow is
0.8
. If it does not rain today, the probability that it will rain tomorrow is
0.7
. If
P
_
1
: denotes the probability that it does not rain today.
P
_
2
: denotes the probability that it will not rain tomorrow, if it rains today.
P
_
3
: denotes the probability that it will rain tomorrow, if it does not rain today.
P
_
4
: denotes the probability that it will not rain tomorrow, if it does not rain today.
(i) Find the value of
P
_
1×
P
_
4-
P
_
2×
P
_
3
(ii) Calculate the probability of raining tomorrow.
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Question 31 (A) – (i) The probability that it rains today is 0.4 . If it rains today, the probability that it will rain tomorrow is 𝟎.𝟖. If it does not rain today, the probability that it will rain tomorrow is 𝟎.𝟕. If 𝑷_𝟏 : denotes the probability that it does not rain today. 𝑷_𝟐 : denotes the probability that it will not rain tomorrow, if it rains today. 𝑷_𝟑 : denotes the probability that it will rain tomorrow, if it does not rain today. 𝑷_𝟒 : denotes the probability that it will not rain tomorrow, if it does not rain today. (i) Find the value of 𝑷_1×𝑷_4−𝑷_2×𝑷_3 Given
Probability it rains today = 0.4
Probability if it rains today, it will rain tomorrow = 0.8
Probability if it does not rain today, it will rain tomorrow = 0.8
Finding 𝑷_𝟏
𝑷_𝟏 : denotes the probability that it does not rain today.
Now,
𝑷_𝟏 = 1 – Probability it rains today
= 1 – 0.4
= 0.6
Finding 𝑷_𝟐
𝑷_𝟐 : denotes the probability that it will not rain tomorrow, if it rains today.
Now,
𝑷_𝟐 = 1 – Probability( it rains tomorrow if it rains today)
= 1 – 0.8
= 0.2
Finding 𝑷_𝟑
𝑷_𝟑 : denotes the probability that it will rain tomorrow, if it does not rain today.
This is given to us,
∴ 𝑷_𝟑 = 0.7
Finding 𝑷_𝟒
𝑷_𝟒 : denotes the probability that it will not rain tomorrow, if it does not rain today
Now,
𝑷_𝟒 = 1 – Probability( it rains tomorrow if it does not rain today)
= 1 – 0.7
= 0.3
Now,
𝑷_𝟏×𝑷_𝟒−𝑷_𝟐×𝑷_𝟑= 0.6 × 0.3 – 0.2 × 0.7
= 0.18 – 0.14
= 0.04
Question 31 (A) – (ii) The probability that it rains today is 0.4 . If it rains today, the probability that it will rain tomorrow is 𝟎.𝟖. If it does not rain today, the probability that it will rain tomorrow is 𝟎.𝟕. If 𝑷_𝟏 : denotes the probability that it does not rain today. 𝑷_𝟐 : denotes the probability that it will not rain tomorrow, if it rains today. 𝑷_𝟑 : denotes the probability that it will rain tomorrow, if it does not rain today. 𝑷_𝟒 : denotes the probability that it will not rain tomorrow, if it does not rain today. (ii) Calculate the probability of raining tomorrow.Now,
Probability of raining tomorrow
= Probability it rains today × Probability it rains tomorrow if it rains today
+ Probability it does not rain × Probability it rains tomorrow if it rains today
= 0.4 × 0.8 + 0.6 × 0.7
= 0.32 + 0.42
= 0.74
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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