Question

13. Find the probability of getting following when a card is chosen from pack of cards
a)
Red king
b) An Ace
c) A spade​

Answer 1

            $\red\dag$ SOLUTION $\blue\dag$

$\boxed{\sf Probability \; of \;an \; event = \dfrac{Number \;of \; favorable \;outcomes}{Total \;number \;of \;outcomes} }$

Here ,

∵ We know that a pack of card contains 52 cards.

∴ The total number of outcomes = 52.

Red king

There are two red kings in a pack of cards.

∴ Number of favorable outcomes = 2.

$\implies \sf P(Red \; King) = \dfrac{2}{52}$

$\implies \sf P(Red \; King) = \dfrac{1}{26}$

An Ace

There are four aces in a pack of cards.

∴ Number of favorable outcomes = 4

$\implies \sf P(Ace) = \dfrac{4}{52}$

$\implies \sf P(Ace) = \dfrac{1}{13}$

A Spade

There are 13 cards of spade in a pack of cards.

∴ Number of favorable outcomes = 13.

$\implies \sf P(Spade) = \dfrac{13}{52}$

$\implies \sf P(Spade) = \dfrac{1}{4}$