11.1 Two events, A and B, are such that:
- Events A and B are independent
- P(not A) = 0,4
- P(B) = 0,3
Calculate P(A and B) - NSC Mathematics - Question 11 - 2021 - Paper 1
Question 11
11.1 Two events, A and B, are such that:
- Events A and B are independent
- P(not A) = 0,4
- P(B) = 0,3
Calculate P(A and B).
11.2 A survey was conducted among 15... show full transcript
Worked Solution & Example Answer:11.1 Two events, A and B, are such that:
- Events A and B are independent
- P(not A) = 0,4
- P(B) = 0,3
Calculate P(A and B) - NSC Mathematics - Question 11 - 2021 - Paper 1
Step 1
Calculate P(A and B)
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Answer
To calculate P(A and B), we use the formula for independent events:
P(A and B)=P(A)×P(B)
We first find P(A):
P(A)=1−P(notA)=1−0.4=0.6
Now substitute into the equation:
P(A and B)=0.6×0.3=0.18
Step 2
Determine a, the probability that a learner, selected at random, participates in all three activities
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Answer
Let a be the probability that a learner participates in all three activities:
Total probability of taking part in at least one activity is 0.7.
Considering all probabilities:
0.24+0.14+a+0.12+0.02+0.15=0.7
Solving this:
a + 0.67 = 0.7\
a = 0.7 - 0.67 = 0.03$$
Step 3
Determine m, the probability that a learner, selected at random, does not participate in any of the three activities
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Answer
Using the total probability of 1:
m=1−0.7=0.3
Step 4
How many learners play only chess?
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Answer
From the Venn diagram, let b be the number of learners who play only chess:
We know that both the learners that only debate and only chess are equal:
\text{Therefore, using the total number of learners (150): }
\ b = 0.04 \times 150 = 6$$
