# A card is drawn at random from a well-shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

Last updated date: 20th Mar 2023

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Answer

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Hint: Find the total number of outcomes. Eliminate the red cards, and the queens in the black cards for the favorable outcomes. Using the definition and formula of probability find the result.

Complete step-by-step answer:

Probability of an event (P) = $\dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$

Total number of cards = total number of outcomes = 52

Let E be an event where one card is picked randomly from the pack is neither a red card nor a queen.

Now, the card should not be a red card hence the card picked must be from the remaining black cards.

Number of red cards = Number of black cards = 26

Thus, favorable outcomes are 26.

Now, the card cannot be queen. There are 2 queens in the black cards.

Thus the favorable outcome = 26 – 2

= 24.

∴P(getting neither a Red nor a Queen) = 24/52

⟹P(E) = $\dfrac{6}{{13}}$

Note: The key point in such problems is to look for the perfect formula and proceed accordingly. Counting the total possible outcomes and total favorable outcome is crucial.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one.

Complete step-by-step answer:

Probability of an event (P) = $\dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$

Total number of cards = total number of outcomes = 52

Let E be an event where one card is picked randomly from the pack is neither a red card nor a queen.

Now, the card should not be a red card hence the card picked must be from the remaining black cards.

Number of red cards = Number of black cards = 26

Thus, favorable outcomes are 26.

Now, the card cannot be queen. There are 2 queens in the black cards.

Thus the favorable outcome = 26 – 2

= 24.

∴P(getting neither a Red nor a Queen) = 24/52

⟹P(E) = $\dfrac{6}{{13}}$

Note: The key point in such problems is to look for the perfect formula and proceed accordingly. Counting the total possible outcomes and total favorable outcome is crucial.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one.

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