Question Bank - Mathematics

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From two well shuffled pack of cards what is the probability of getting one Jack from the first one and a King from the second?

A.
\(\frac{1}{{13\, \times \,13}}\)
B.
\(\frac{{2\, \times \,3}}{{26\, \times \,25}}\)
C.
\(\frac{1}{{52\, \times \,52}}\)
D.
\(\frac{{4 \times 3}}{{52\, \times \,51}}\)

Solution:

Given:The number of cards in the first pack of cards = 52The number of Jack in a pack of cards = 4The number of cards in the second pack of cards = 52The number of King in a pack of cards = 4Formula used:P = P(A) × P(B)Where, P(A) and P(B) are the probability of happening event A and event B (both are independent.)P, is the required probability of happening event A and event BCalculation:The probability of selecting one Jack from the first pack of cards \(\frac{4}{52} = \frac{1}{13}\)The probability of selecting one King from the second pack of cards \(\frac{4}{52} = \frac{1}{13}\)Since both events are independent,Therefore, The required probability = \(\frac{1}{13}\) × \( \frac{1}{13}\)? The probability of getting one Jack from the first one and a King from the second is \(\frac{1}{13 × 13}\).

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