Question

1. You draw a card from an ordinary 52 card deck. Let P (J) be the probability of drawing a jack. Let P K) be the probability of drawing a king. Let P (H) be the probability of drawing a heart. You draw one card. Answer each of the following based these probabilities.
   1. For a single trial, explain which events [P (J), P (K), P (H)] are mutually exclusive and which events are not? Explain.
2. 2. For a single draw, state the probability of the draw being a jack or king or heart in symbols.
   3. For a single draw, determine the probability of the draw being a jack or king or heart. Give the solution as a numerical fraction.

Answer 1

There are 52 cards in a deck among those cards 4 jack , 4 king and 13 hearts.

Then probability of drawing a jack is P(J) = 4/52 = 1/13.

Probability of drawing a king is P(K) = 4/52 = 1/13.

Probability of drawing a Heart is P(H) = 13/52 = 1/4.

a) Here event J and K are mutually exclusive as P(J K) = 0 (no common element exists)

Where as K and H are not mutually exclusive, J and H are also not mutually exclusive. Beacuse there is a king of hearts and also a jack of hearts is exists.

b) there are total 13 + 3 + 3 = 19 cases favourable to the event J K H ( 13 hearts including 1 king and 1 jack and remaining 3 jack and 3 king )

So P(J K H) = 19/52.