IndiaSMart is a retail shop that accepts either a Rupay credit card, or a Visa credit card. 31 percent of IndiaSMart’s customers carry a Rupay credit card, 44 percent of its customers carry a Visa credit card, while 18 percent of its customers carry a Rupay credit card as well as a Visa credit card. What is the probability that a customer carries at least one of the two, i.e. either a Rupay or a Visa credit card?
Show Hint
- 0.75
- 0.93
- 0.57
- 0.49
The Correct Option is C
Solution and Explanation
Step 1: Understand the problem
We are looking for the probability that a customer carries at least one of the two credit cards (Rupay or Visa). This is the union of two events, so we use the formula for the union of two sets:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Where:
- P(A) is the probability of carrying a Rupay card (0.31),
- P(B) is the probability of carrying a Visa card (0.44),
- P(A ∩ B) is the probability of carrying both cards (0.18).
Step 2: Apply the formula
Substitute the given values into the formula:
\[ P(A \cup B) = 0.31 + 0.44 - 0.18 = 0.57 \]
Thus, the probability that a customer carries at least one of the two credit cards is 0.57.
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