Question

A pack of cards is shuffled and a card picked at random, what is the probability of getting
(i) red card
(ii) black face card
(iii) an ace

Answer 1

Hint: Probability of an event to occur in an experiment is equal to the ratio of the outcomes in which this event happens to the total number of outcomes of the experiment. In other words, it is equal to the ratio of favourable outcomes to the total number of outcomes.

Complete step by step solution:
Let us first understand what is meant by the term probability of happening of an event. The term probability of an event happening tells us about the extent or how many times it is likely to happen in a given number of tries.For example, if we throw a dice of six faces, then the probability of a number to come on the top of the dice tells us about the extent to which that is likely to occur.

Probability of an event to occur in an experiment is equal to the ratio of the outcomes in which this event happens to the total number of outcomes of the experiment. A pack of cards contains 52 total cards.Therefore, when we pick a card from the set there can be 52 different outcomes.
(i) A pack of cards contains 13 red cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of getting a red card is $\dfrac{13}{52}=\dfrac{1}{4}$.
(ii) A pack of cards contains 13 black cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of a getting a black card is $\dfrac{13}{52}=\dfrac{1}{4}$
(iii) A pack of cards contains 4 black cards. Therefore, out of those 52 outcomes, 4 outcomes are required. Hence, the probability of getting an ace is $\dfrac{4}{52}=\dfrac{1}{13}$.

Note: Note that probability is not always sure or it doesn’t guarantee that the specific event will surely happen in those number of trials. This means that if the probability of getting an ace card does not mean that in four tries we will surely get an ace.Probability just tells us about how likely the event may happen.