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) ā (
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 itĀ 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
_
1Ć
P
_
4-
P
_
2Ć
P
_
3
(ii) Calculate the probability of raining tomorrow.
Question 31 (A) ā (i) The probability that it rains today is 0.4 . If it rains today, the probability that it will rain tomorrow is š.š. If it does not rain today, the probability that it will rain tomorrow is š.š. If š·_š : denotes the probability that it does not rain today. š·_š : denotes the probability that it will not rain tomorrow, if it rains today. š·_š : denotes the probability that it will rain tomorrow, if it does not rain today. š·_š : denotes the probability that it will not rain tomorrow, if it does not rain today. (i) Find the value of š·_1Ćš·_4āš·_2Ćš·_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 š·_š
š·_š : denotes the probability that it does not rain today.
Now,
š·_š = 1 ā Probability it rains today
= 1 ā 0.4
= 0.6
Finding š·_š
š·_š : denotes the probability that it will not rain tomorrow, if it rains today.
Now,
š·_š = 1 ā Probability( it rains tomorrow if it rains today)
= 1 ā 0.8
= 0.2
Finding š·_š
š·_š : denotes the probability that it will rain tomorrow, if it does not rain today.
This is given to us,
ā“ š·_š = 0.7
Finding š·_š
š·_š : denotes the probability that it will not rain tomorrow, if it does not rain today
Now,
š·_š = 1 ā Probability( it rains tomorrow if it does not rain today)
= 1 ā 0.7
= 0.3
Now,
š·_šĆš·_šāš·_šĆš·_š= 0.6 Ć 0.3 ā 0.2 Ć 0.7
= 0.18 ā 0.14
= 0.04
Question 31 (A) ā (ii) The probability that it rains today is 0.4 . If it rains today, the probability that it will rain tomorrow is š.š. If it does not rain today, the probability that it will rain tomorrow is š.š. If š·_š : denotes the probability that it does not rain today. š·_š : denotes the probability that it will not rain tomorrow, if it rains today. š·_š : denotes the probability that it will rain tomorrow, if it does not rain today. š·_š : 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 Ć Probability it rains tomorrow if it rains today
+ Probability it does not rain Ć Probability it rains tomorrow if it rains today
= 0.4 Ć 0.8 + 0.6 Ć 0.7
= 0.32 + 0.42
= 0.74
Made by
Davneet Singh
Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.
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