Question
Download Solution PDFA pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A pack of cards contains 4 aces, 4 kings, 4 queens, and 4 jacks.
Total number of cards = 16
Formula used:
Probability of an event = (Number of favorable outcomes) / (Total number of outcomes)
Calculation:
Number of ways to draw 2 cards out of 16:
16C2 = (16 × 15) / (2 × 1) = 120
Number of ways to draw 2 cards such that neither is an ace:
Number of non-ace cards = 16 - 4 = 12
12C2 = (12 × 11) / (2 × 1) = 66
Number of ways to draw 2 cards such that at least one is an ace:
Number of favorable outcomes = Total ways - Ways with no ace
⇒ 120 - 66 = 54
Probability that at least one of them is an ace:
⇒ 54 / 120
⇒ 9 / 20
∴ The probability that at least one of them is an ace is 9/20.
Last updated on May 10, 2025
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