Please answer all 3 ASAP and neatly Thank you 1. From a standard deck of 52 play

Question

Please answer all 3 ASAP and neatly Thank you

1. From a standard deck of 52 playing cards, one card is drawn. Find the probability that it is (6 marks) (a) a queen (b) a red card (c) a spade 2. If the odds that an event E will occur are 23:57, what is the probability that: (4 marks) (a) The event E will occur? (b) The event E will not occur? 3. A ball is drawn from a bag containing 13 red balls numbered 1 - 13 and 5 white balls numbered 14-18. What is the probability that: (6 marks) (a) The ball is not red? (b) The ball is white and odd numbered? (c) The ball is white or odd numbered?

Explanation / Answer

1.

(a) P(Queen) = 4/52= 0.0769

(b) P(Red) = 26/52 = 0.50

(c) P(Spade) = 13/52 = 0.25

2.

odds = wanted outcomes/unwanted outcomes = 23/57

Probability= wanted outcomes/total outcomes

               = 23/(23+57) = 23/80 = 0.2875

3.

(a) P(not red) = 1 - P(red) = 1 - 13/18= 1 - 0.7222 = 0.2778

(b)

Let A = White

B = Odd

By Multiplication Theorem:
P(AB) = P(A) P(B/A)

P(A) = P(White) = 5/18 = 0.2778

P(B/A) = P(Odd given that White) = 2/5 = 0.40

So,

P(AB) = 0.2778 X 0.40= 0.1111

(c)

P(White OR Odd) = P(White) + P(Odd) - P(White & Odd)

                                 = 5/18 + 9/18 - 2/18

                                   = 0.6667

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