# From a deck of cards, if a card is randomly chosen, find the probability of getting a card with $\left( i \right)$A prime number on it, $\left( {ii} \right)$ face on it.

Last updated date: 20th Mar 2023

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Answer

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Hint: Here, we have to use formula to find the required probability of given event P(E)$ = \dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$

Complete step-by-step answer:

Total number of cards$ = 52$

$\left( i \right)$ A prime number on it

As we know a prime number is a number who is divisible by 1 or by itself, therefore prime numbers in the deck$ = \left( {2,3,5,7} \right)$, 1 is not a prime number because a prime number should have factor other than 1, but 1 has only one factor which is itself, so, 1 is not a prime number, so there are 4 prime numbers in each set of a deck of cards

In a deck of cards there are four sets of each number.

Therefore number of favorable outcomes$ = 4 \times 4 = 16$

Therefore probability of getting a prime number on the card$ = \dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}} = \dfrac{{16}}{{52}} = \dfrac{4}{{13}}$

$\left( {ii} \right)$Face on it

As we know there are three face cards in each set of a deck of cards which is (jack, queen, king)

So, in a deck of cards there are four sets of each face card.

Therefore number of favorable outcomes$ = 3 \times 4 = 12$

Therefore probability of getting face on the card

$ = \dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}} = \dfrac{{12}}{{52}} = \dfrac{3}{{13}}$

So, this is the required probability.

Note: In such types of questions first calculate the total number of possible outcomes, then calculate the number of favorable outcomes then divide these two values using the formula which is stated above, we will get the required probability.

Complete step-by-step answer:

Total number of cards$ = 52$

$\left( i \right)$ A prime number on it

As we know a prime number is a number who is divisible by 1 or by itself, therefore prime numbers in the deck$ = \left( {2,3,5,7} \right)$, 1 is not a prime number because a prime number should have factor other than 1, but 1 has only one factor which is itself, so, 1 is not a prime number, so there are 4 prime numbers in each set of a deck of cards

In a deck of cards there are four sets of each number.

Therefore number of favorable outcomes$ = 4 \times 4 = 16$

Therefore probability of getting a prime number on the card$ = \dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}} = \dfrac{{16}}{{52}} = \dfrac{4}{{13}}$

$\left( {ii} \right)$Face on it

As we know there are three face cards in each set of a deck of cards which is (jack, queen, king)

So, in a deck of cards there are four sets of each face card.

Therefore number of favorable outcomes$ = 3 \times 4 = 12$

Therefore probability of getting face on the card

$ = \dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}} = \dfrac{{12}}{{52}} = \dfrac{3}{{13}}$

So, this is the required probability.

Note: In such types of questions first calculate the total number of possible outcomes, then calculate the number of favorable outcomes then divide these two values using the formula which is stated above, we will get the required probability.

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