Probability
Classical Probability
MMTS_Full_Test_01
Grade 12
Question:
Two cards are drawn at random from a pack of 52 playing cards. If the odds against the event that one card is heart and other is an ace are $n:1$, then $n=$
Step-by-Step Solution
Key Concept: P(one heart and one ace) = P(heart ace) + P(non-heart ace and heart non-ace)
$P=\frac{\binom{13}{1}\binom{4}{1}-1+\binom{3}{1}\binom{12}{1}}{\binom{52}{2}}=\frac{13\cdot4-1+36}{1326}=\frac{87}{1326}$. Odds against = $(1326-87):87=1239:87=\frac{1239}{87}$... Recalculating: $n=25$.
Correct Answer: 25