Explanation

To find P(A ∩ M ∩ S), we use the addition rule for three sets:

Formula: P(A ∪ M ∪ S) = P(A) + P(M) + P(S) − P(M ∩ A) − P(M ∩ S) − P(A ∩ S) + P(A ∩ M ∩ S)

Given:

• P(S) = 0.45
• P(M ∩ A) = 0.19
• P(M ∩ S) = 0.15
• P(A ∩ S) = 0.25
• P(M ∪ S) = 0.6
• P(A ∪ S) = 0.84
• P(A ∪ M ∪ S) = 0.9

Step 1: Find P(M) Using P(M ∪ S) = P(M) + P(S) − P(M ∩ S): 0.6 = P(M) + 0.45 − 0.15 P(M) = 0.6 + 0.15 − 0.45 = 0.3

Step 2: Find P(A) Using P(A ∪ S) = P(A) + P(S) − P(A ∩ S): 0.84 = P(A) + 0.45 − 0.25 P(A) = 0.84 − 0.45 + 0.25 = 0.64

Step 3: Apply the three-set addition rule 0.9 = 0.64 + 0.3 + 0.45 − 0.19 − 0.15 − 0.25 + P(A ∩ M ∩ S) 0.9 = 0.8 + P(A ∩ M ∩ S) P(A ∩ M ∩ S) = 0.9 − 0.8 = 0.10

Therefore, the probability that a customer chooses all three juices (apple, mango, and passion fruit) is 0.10.