Question

We have 5 cards as ten, jack, queen, king and ace of a diamond are well-shuffled with their faces downwards, 1 card is then picked up at random.
(a) What is the probability that drawn card is a queen?
(b) If the queen is drawn and put aside and a second card is drawn. Find the probability that the second card is an ace, a queen? Explain

Answer 1

Hint: We are given that we have 5 chards and we have to find the probability, we will use the formula \[\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}\] and then we will find the favorable outcomes and the total outcomes in each case. Then using the above formula, we will find our required probability.

Complete step by step answer:
We are given that we have 5 cards that are as follows: Ten, Jack, Queen, King, and Ace of Diamond. We are asked to find the probability. We know that the probability is the possibility of the occurrence of some event. Probability is defined as \[\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}\] where favorable outcome means the number of outcomes which is related to the event.
(a) Now, first we are said that one card is taken out and we have to find the probability of the card is a queen. Now, we have just 5 cards in total. So,
Total Outcomes = 5……(i)
Now, out all the 5 cards, our favorable is getting a queen. Since we have just 1 queen out of all, so we get,
Number of favorable outcomes = 1……(ii)
So, using (i) and (ii), we get,
\[P\left( \text{getting a queen} \right)=\dfrac{1}{5}\]
(b) Secondly we are said that the queen is picked and taken aside from our given cards. So, earlier we were having 5 cards. Now we had 1 less, so we get,
Total cards = 4…..(iii)
Now, we will look to find the probability of getting an ace. Out of the remaining four, we have 1 ace, so,
Number of favourable outcomes = 1…..(iv)
So, using (iii) and (iv), we get,
\[P\left( \text{getting an ace} \right)=\dfrac{1}{4}\]
Now, we have to find the probability of getting a queen. As mentioned, 1 queen is taken out and put aside. So, we get,
Number of Queen left = 0
So, the number of favorable outcomes = 0……(v)
So, using (iii), (iv), and (v), we get,
\[P\left( \text{Queen} \right)=\dfrac{0}{4}=0\]

Note:
Students need to remember in part (b) that one card is taken out so we have to reduce the total outcomes by 1. Always remember that the probability is never greater than 1, also it is never less than 0. If the favorable outcome is not available so in such cases, the probability is always 0.