The topic probability is one of the most important topic for Elitmus test. Practice these questions on the topic of probability.

(i) List the sample space S.

(ii) List the event E, \toss a head and spin an A or B."

(iii) Find P(E).

(iv) List E.

(v) Find P(E).

(i) S = {HA;HB;HC; TA; TB; TC}

(ii) E = {HA;HB}

(iii) P(E) =2/6=1/3

(iv) E = {HC; TA; TB; TC}

(v) P(E) =4/6=2/3

(i) A red card.

(ii) Not a face card.

(iii) The queen of spades.

(iv) A seven or a black card.

(i) 26/52=1/2

(ii) 40/52=10/13

(iii) 1/52

(iv) P(7) + P(black) U P(7 \ black) =4/52+26/52 U 2/52=28/52=7/13

(i) In favour of getting a 7?

(ii) Against getting a prime number?

(iii) Against getting a number less than 9?

(i) 1:9

(ii) 6:4 (prime numbers are 2,3,5,7)

(iii) 2:8

.65(70; 000) + :35(30; 000) = 35; 000

**Question:**For the experiment \toss a coin and spin a spinner with three equal sectors labeled A, B, and C."(i) List the sample space S.

(ii) List the event E, \toss a head and spin an A or B."

(iii) Find P(E).

(iv) List E.

(v) Find P(E).

**Answer:**(i) S = {HA;HB;HC; TA; TB; TC}

(ii) E = {HA;HB}

(iii) P(E) =2/6=1/3

(iv) E = {HC; TA; TB; TC}

(v) P(E) =4/6=2/3

**Question:**A card is drawn at random from a deck of 52 playing cards. What is the probability of drawing each of the following?(i) A red card.

(ii) Not a face card.

(iii) The queen of spades.

(iv) A seven or a black card.

**Answer:**(i) 26/52=1/2

(ii) 40/52=10/13

(iii) 1/52

(iv) P(7) + P(black) U P(7 \ black) =4/52+26/52 U 2/52=28/52=7/13

**Question:**If you draw a whole number from 1 to 10 at random, what are the odds:(i) In favour of getting a 7?

(ii) Against getting a prime number?

(iii) Against getting a number less than 9?

**Answer:**(i) 1:9

(ii) 6:4 (prime numbers are 2,3,5,7)

(iii) 2:8

**Question:**In a proposed business venture, Stephanie estimates there is a 65% chance she will make $70; 000 and a 35% chance she will lose $30; 000. Determine Stephanie's expected value.**Answer:**.65(70; 000) + :35(30; 000) = 35; 000

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