Question

three cards are drawn simultaneously from a well shuffled pack of 52 cards.What is the probability that two of them are even-numbered cards and one is an odd-numbered card?
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Answer 1

Answer:

Answer is 13/34

Step-by-step explanation:

total outcome = selecting 3 from 52 = 52C3 = 22100

possible outcome = selecting 2 from 26 and 1 from other 26

                                26C1 + 26C2 = 8450

probability = 8450/22100 = 13/34 = 0.3

Answer 2

Given is a well-shuffled pack of 52 cards, find the probability of picking two even and one odd-numbered card simultaneously.

Explanation:

• In an ideal pack of fifty-two cards there are $4$ cards marked by each number from $2-10$.
• Hence the number of even and odd-numbers between $2-10$ are $5, 4$ respectively.
• Hence, the total number of even and odd-numbered cards in a pack are, $n(E)=20,\ \ n(O)=16$  
• Now the probability of getting two even-numbered cards simultaneously is,
•                           $->P(E)=\frac{^{20}C_2}{^{52}C_2} \\->P(E)=0.143$  
• Now the probability of getting one odd-numbered card is,
•                           $->P(O)=\frac{^{16}C_1}{^{52}C_1} \\->P(O)=0.308$  
• Now the probability of getting two even and one odd-numbered card is simply the product of both individual probabilities as they are independent events.
• Hence we have,  
•                          $P(2Es\ and\ O)=P(2Es)P(O) \\->P(2Es\ and\ O)=0.143(0.308)\\->P(2Es\ and\ O)=0.044$  
• The probability of getting two even and one odd-numbered card is nearly $0.044$.