PROBABILITY

 

1.                   One card is drawn at random from a normal pack of 52 cards.

What is the probability of drawing

(i)                  A red card?

(ii)                A black card?

(iii)               A heart?

(iv)              A picture card?

(v)                The ace of spades?

 

2.                   A coin is tossed 3 times. What is the probability of tossing

(i)                  Three heads?

(ii)                Two heads and a tail?

(iii)               At least one head?

(iv)              No heads.

 

3.                   A drawer contains 10 black socks and 10 brown socks. If Josh goes to the drawer in the dark and chooses two socks at random, what is the probability of him choosing

(i)                  Two black socks?

(ii)                A matching pair?

 

4.                   The drawer now contains 12 black socks and 8 brown socks. If Josh again goes to the drawer in the dark and chooses two socks at random, what is the probability of him choosing

(i)                  Two black socks?

(ii)                A matching pair?

 

5.                   Two dice are thrown and the score is taken as the sum of the dots on the two uppermost faces.

(i)                  Draw a grid showing all of the possible outcomes. Use your grid to determine

(ii)                The probability of throwing 12.

(iii)               The probability of throwing an even total.

(iv)              The probability of throwing a total greater than 7.

(v)                The probability of throwing a 1 on at least one of the dice?

 

Answers:

1.         (i)           (ii)                (iii)               (iv)              (v)

2.         (i)           (ii)                (iii)               (iv)

3.         (i)         (ii)

4.         (i)         (ii)

5.         (i)

 

1

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2

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5

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11

6

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12

            (ii)        (iii)               (iv)              (v)

 

 

 

 

MORE PROBABILITY

 

  1. Nathan has 4 cards, each showing one of the digits 1, 2, 3, 4. If he lays 3 of the cards down to form a three digit number, what is the probability of the number being

(i)      Even?

(ii)    Divisible by 4?

(iii)   Less than 120?

(iv)  Greater than 230?

 

  1. Greg bought two tickets in a raffle in which 1000 tickets were sold. What is the probability that Greg will win

(i)      First prize

(ii)    First and second prize

(iii)    Second prize

(iv)  No prize

(v)    Explain why answers (i) + (ii) + (iii) + (iv) =1

 

  1. A family has 4 children. What is the probability that

(i)      All 4 are girls?

(ii)    There are 2 girls?

(iii)   At least one is a girl?

(iv)  There are no girls?

 

  1. In a class of 28 students, 14 have chosen soccer for sport, 8 have chosen tennis and 6 have chosen softball. If two students are chosen at random from the class, what is the probability that

(i)      They both play tennis?

(ii)    One plays tennis and one plays soccer?

(iii)    Neither plays tennis?

 

  1. A bag contains 5 red marbles, 3 white marbles and two blue marbles. If two marbles are drawn from the bag at random, what is the probability that

(i)      The first marble drawn is blue?

(ii)    The first marble drawn is white?

(iii)   Both the first and second marbles drawn are white?

(iv)   Both marbles are red?

(v)    Neither marble is white?

 

Answers:

 

1.   (i)     (ii)    (iii) 0     (iv)

 

2.   (i)  (ii)     (iii)            (iv)     (v) Answers (i) to (iv) represent all possible outcomes. All possible outcomes add to 1.

 

3.   (i)    (ii)    (iii)              (iv)

 

4.   (i)   (ii)              (iii)

 

5.   (i)     (ii)               (iii) (iv)               (v)

 

 

 

 

 

EVEN MORE PROBABILITY

 

  1. The Ladies’ Committee made 100 lucky dips for the school fete. 50 of the lucky dips contained a comic and a ring, 30 contained a comic and a badge and the remainder contained a comic and a whistle. Lauren and Emma each bought a lucky dip. What is the probability that

(i)                  Lauren’s lucky dip contains a whistle?

(ii)                Emma’s lucky dip contains a comic?

(iii)               Both Lauren’s and Emma’s lucky dip contain a ring?

(iv)              Neither Lauren’s nor Emma’s lucky dip contain a badge?

(v)                Lauren’s lucky dip contains a ring and Emma’s lucky dip contains a badge?

 

  1. Rachael took the 4, 5, 6, 7 & 8 of hearts out of a pack of cards and then placed three of them on the table to make a 3 digit number. What is the probability of the number being

(i)                  Even?

(ii)                Odd?

(iii)               Divisible by 5?

(iv)              Greater than 600?

(v)                Less than 600?

(vi)              Greater than 750?

 

  1. The teacher had a strange way of randomly checking the students’ maths homework. He had two dice, one red and the other white. At the beginning of each period he would roll the dice three times to form three two digit numbers. The first digit was the value shown on the red die (die is singular of dice but mie is not the singular of mice) and the second digit, the number shown on the white die.

(i)                  How many two digit numbers could the teacher form?

(ii)                If he allocated each student in the class of 30, a different two digit number, what is the probability of Sarah, a member of the class, being allocated the number 63?

(iii)               What is the probability that the first number that the teacher rolls has not been allocated to any student?

(iv)              What is the probability that the first two numbers that the teacher rolled were the same?

(v)                What is the probability that the three numbers that the teacher rolls have not been allocated so that the teacher does not check anybody’s homework?

 

  1. Tom, Jim and Gus each selected 3 cards with letters on them to make up their names. Gus shuffled the 9 cards and then chose 3 at random. What is the probability that

(i)                  He could spell his own name with the letters chosen?

(ii)                He could spell the name “Tom” with the letters chosen?  

 

Answers:         1. (i) , (ii) 1, (iii) , (iv) , (v)                       

 

2. (i) , (ii) , (iii) , (iv) , (v) , (vi)

 

                        3. (i) 36, (ii) , (iii) , (iv) , (v)      

                       

                        4. (i) , (ii)