Question

A card is drawn at random from a well shuffled deck of 52 playing cards. Find the probability that the card drawn is a card of spade or an ace.

Answer 1

Given:

A well shuffled standard deck of 52 cards.

Event: the drawn card is a spade or an ace.

Step-wise calculation:

1. Total number of equally likely outcomes = 52.

2. Number of spades = 13.

3. Number of aces = 4 (one of which is the ace of spades).

4. Use inclusion–exclusion to avoid double counting:

Number of favourable outcomes

= N(spade) + N(ace) – N(spade ∩ ace)

= 13 + 4 – 1

= 16

5. Probability = `"Favourable outcomes"/"Total outcomes"`

= `16/52`

= `4/13`

= 0.3077

Required probability = `4/13` about 0.3077.