11.1 Two events, A and B, are such that: - P(A) = 0,4 - P(A or B) = 0,52 - A and B are mutually exclusive Calculate P(B) - NSC Mathematics - Question 11 - 2024 - Paper 1

From the Venn diagram, the probability of buying a sandwich (S) is given as:

$P(S) = 0,04 + 0,01 + 0,09 + 0,20 = 0,34$

To find this probability, we can add up the probabilities of the relevant combinations:

• Buying two items (C and S): $0,04 + 0,01 + 0,03 + 0,20 = 0,1$
• Buying all three items: $0,03 + 0,20 = 0,23$

So, total probability:

$P(\text{at least two}) = 0,10 + 0,23 = 0,33$

Using the complementary rule, we can find the probability of not buying any items:

$P(\text{not any}) = 1 - P(\text{at least one item})$

From the probabilities:

$P(\text{at least one}) = 1 - (0,04 + 0,01 + 0,03 + 0,09 + 0,20) = 0,57$

Thus:

$P(\text{not any}) = 1 - 0,57 = 0,43$