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 August 14, 2026 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.
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
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