A basket contains 8 red balls, 10 blue balls, and 2 white balls. One ball is sel

Question

A basket contains 8 red balls, 10 blue balls, and 2 white balls. One ball is selected at random from the jar. a) What is the probability that the ball is red? b) What is the probability that the ball is blue or white? c) What is the probability that the ball is not white? A single card is drawn from a standard 52 card deck. a) Find the probability that the card is a king. b) Find the probability that card is a spade. c) Find the probability that the card is a king or a spade. d) Find the probability that the card is a king and a spade.

Explanation / Answer

Q.4)

A basket contains 8 red balls, 10 blue balls, and 2 white balls. So there are total of 20 balls.

One ball is selected at random form the jar.

a)

Probability that the ball is red is,

P (Red ball) = 8/20 = 0.4

b)

Probability that the ball is blue or white is,

P (Blue ball or White ball) = (10/20) + (2/20) = 12/20 = 0.6

c)

Probability that the ball is not white is,

P (Blue ball or White ball) = 1 – (2/20) = 18/20 = 0.9

Q.5)

A standard deck of cards contain 52 cards. In 52 cards, there are 26 red and 26 black cards. There are 13 cards of 4 suits namely Heart, Diamond, Club and Spade. It also included 12 face cards, 4 cards of each suit.

a)

We know that deck of cards contains 4 Kings. Hence probability that the card is King is,

P (card is a king) = 4/52 = 0.0769

Hence probability that the card is King is 0.0769.

b)

We know that deck of cards contains 13 spade cards. Hence probability that the card is Spade is,

P (card is a spade) = 13/52 = 0.25

Hence probability that the card is Spade is 0.25.

c)

We know that deck of cards contains 4 Kings and 13 Spades. One card King of Spade. Hence we can calculate the probability as ->

P (the card is King or Spade)

= P (King) + P (Spade) – P (King and Spade)          

= (4/52) + (13/52) – (1/52)

= 16/52

Hence probability that the card is King or Spade is 0.3077.

d)

We know that deck of cards contains 4 Kings and 13 Spades. Only one card both King and Spade.

P (the card is King and Spade) = 1/52 = 0.0192

Hence probability that the card is King and Spade is 0.0192.

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