Question

Data is gathered on a randomly selected Saturday on the shoppers at Target The probability that a shopper is drinking Starbucks is 25%, while the probability they have kids with them is 65%, and the probability that they have both is 15%. What is the probability that the shopper will not have Starbucks and not have kids with them? (A) 10% (B) 15% (E) 60% (C) 25% lo (D) 50% sto County 0.20

Answer 1

The probability that a Target shopper will not be drinking Starbucks and not have kids with them is calculated using the principle of complementary probabilities, yielding an answer of 25%.

Step-by-step explanation:

To calculate the probability that a shopper at Target will not be drinking Starbucks and also not have kids with them, we can use the principle of complementary probabilities. The complementary probability of an event is 1 minus the probability of the event occurring.

Given:

• The probability that a shopper is drinking Starbucks (S) is 25%, or P(S) = 0.25.
• The probability that they have kids with them (K) is 65%, or P(K) = 0.65.
• The probability that they have both Starbucks and kids with them is 15%, or P(S ∩ K) = 0.15.

To find the probability of neither, we use:

P(neither) = 1 - P(S ∪ K)

But first, we need to find P(S ∪ K) by using the formula:

P(S ∪ K) = P(S) + P(K) - P(S ∩ K)

Plugging in the values we get:

P(S ∪ K) = 0.25 + 0.65 - 0.15 = 0.75

Now, we calculate the complementary probability:

P(neither) = 1 - P(S ∪ K) = 1 - 0.75 = 0.25 or 25%

Therefore, the correct answer is (C) 25%.

Answer 2

To find the probability that a shopper is neither drinking Starbucks nor with kids at Target, we calculate 1 - (Probability of Starbucks + Probability of Kids - Probability of Both), which equals 25%.

Step-by-step explanation:

The question asks for the probability that a shopper at Target is neither drinking Starbucks nor accompanied by kids. To calculate this, we can use the complementary probability of the sum of all given probabilities and then subtract the intersection which is already included in both probabilities. The formula we use is:

P(Not Starbucks and Not Kids) = 1 - (P(Starbucks) + P(Kids) - P(Both Starbucks and Kids))

Substituting the given values:

P(Not Starbucks and Not Kids) = 1 - (0.25 + 0.65 - 0.15)

P(Not Starbucks and Not Kids) = 1 - 0.75

P(Not Starbucks and Not Kids) = 0.25 or 25%

Therefore, the correct answer is (C) 25%.