A coin is tossed. What are all possible outcomes? (i) Two coins are t

1.	A coin is tossed. What are all possible outcomes? (i) Two coins are tossed simultaneously. What are all possible outcomes? (ii) A die is thrown. What are all possible outcomes? (iii) From a well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?
Answer» (i) A coin has two sides a head(H) and a tail(T). ∴ There are X^m possible outcomes. [Where X is number of outcomes when a coin is tossed and m is number of coins.] That is 2¹ = 2 and they are H, T. ∴ All possible outcomes are H, T. (ii) A coin has two sides a head(H) and a tail(T), and there are two such coins. ∴ There are X^m possible outcomes. [Where X is number of outcomes when a coin is tossed and m is number of coins.] That is 2² = 4 and they are HH, HT, TH, TT ∴ All possible outcomes are HH, HT, TH, TT. (iii) A die has 6 faces and they are 1, 2, 3, 4, 5, 6 ∴ All possible outcomes are 1, 2, 3, 4, 5, 6. (iv) A deck of cards have a total of 52 cards. ∴ Number of possible outcomes are 52.

A coin is tossed. What are all possible outcomes? (i) Two coins are tossed simultaneously. What are all possible outcomes? (ii) A die is thrown. What are all possible outcomes? (iii) From a well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?

Answer»

(i) A coin has two sides a head(H) and a tail(T).

∴ There are X^m possible outcomes.

[Where X is number of outcomes when a coin is tossed and m is number of coins.]

That is 2¹ = 2 and they are H, T.

∴ All possible outcomes are H, T.

(ii) A coin has two sides a head(H) and a tail(T), and there are two such coins.

∴ There are X^m possible outcomes.

[Where X is number of outcomes when a coin is tossed and m is number of coins.]

That is 2² = 4 and they are HH, HT, TH, TT

∴ All possible outcomes are HH, HT, TH, TT.

(iii) A die has 6 faces and they are 1, 2, 3, 4, 5, 6

∴ All possible outcomes are 1, 2, 3, 4, 5, 6.

(iv) A deck of cards have a total of 52 cards.

∴ Number of possible outcomes are 52.