Question

Which one of the following is an impossible event?
This question has multiple correct options.
A. Rolling a die to get 4.
B. Tossing a coin to get a tail.
C. Choosing 4 face cards of spades.
D. Rolling a die for 7.

Answer 1

Hint: The probability of an impossible event is 0.
(i)Probability of an event is defined as $\text{P(E)}=\dfrac{\text{No. of Favorable Outcomes}}{\text{Total No. of Outcomes}}$ .
(ii)Dice/Die: A dice is a cube which has six faces, numbered from 1 to 6.
(iii)Coin: A coin has two sides, Head and Tail.
(iv)Cards: In a deck of 52 cards, there are 13 cards of each suite (Heart, Club, Diamond and Spades). The cards from 1 to 10 are called 'Numbered cards' and the remaining three cards in each suit are called 'Face cards' (Jack, Queen and King) because they have a human face printed on them. Number 1 is also called an Ace (A).
Complete step-by-step answer:
Let us look at the answer options one by one and check if they are correct:
A. Rolling a die to get 4.: Since, a dice has faces numbered from 1 to 6, it is possible to get a 4 in rolling a die.
B. Tossing a coin to get a tail.: Since, a coin has two sides which are called a head and a tail, it is possible to get a tail in a toss of a coin.
C. Choosing 4 face cards of spades.: In a deck of 52 cards, there are only 3 face cards in any suite. Therefore, it is not possible to choose 4 cards of the suite called Spades.
D. Rolling a die for 7.: As seen in option A above, there are only 1 to 6 possible outcomes for a roll of dice. It is not possible to roll a 7.
Answer options C. and D. are correct.

Note: Certain Event: An event which will always occur is called a certain event. The probability of a certain event is 1. i.e. P(E) = 1.
Impossible Event: An event which cannot happen is called an impossible event. For an example, getting both head and tail in simultaneously in tossing a coin. The probability of an impossible event is 0, i.e. P(E) = 0.