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Probability - Arrays.
Test Yourself 1.


 

One dimensional array  
   
   
Union of events. 5. Fifty identical cards numbered 1 to 50 are shuffled so their order is now randomised. One card is drawn at random.

What is the probability that the number on the card selected is less than 30 or divisible by 5?

Answer. 34/50.
   
   
Two dimensional array 1. Two dice are biassed so that the probability of rolling a six is 3/8 and the probability of rolling each other number is 1/8.

Find the probability of:

(i) rolling a double 6.

(ii) rolling the two dice so that neither is a six.

(iii) only one six appears when the two dice are rolled.

Answer.(i) Pr(66) = 9/64.
(ii) Pr(no 6) = 53/64.
(iii) Pr (only 1 six) = 15/32.
  2. A fair dice is rolled twice. Find the probability that:

(i) the score in the second roll is greater than that on the first roll.

(ii) The total of the two scores is 7 or 11.

Answer.(i) Pr (2nd score higher) = 5/12.
(ii) Pr (7 or 11) = 2/9.
  3. Two ordinary dice are rolled. The score is the sum of the numbers on the top faces.

(i) What is the probability that the score is 10?

(ii) What is the probability that the score is not 10?

Answer.(i) Pr (10) = 1/12.
(ii) Pr (not 10) = 11/12.
  4. Two ordinary dice are rolled and the score is calculated by adding the numbers on the top faces.

(i) What is the probability that the score is 4?

(ii) What is the probability that the score is not 4?

(iii) What is the probability that both dice show the same number?

Answer.(i) Pr (4) = 1/12.
(ii) Pr (not 4) = 11/12.
(iii) Pr (pair) = 1/6.
  5. A die numbered 1 to 6 on its six faces is rolled twice. The sum of the numbers on the upper face are added together.

(i) What is the probability that the sum is greater than 9?

(ii) It is known that 5 appears on at least one of the dice in the two throws. What is the probability that the sum is greater than 9?

Answer.(i) Pr (greater than 9) = 1/6.
(ii) Pr (greater than 6| a 5) = 4/11.
  6. A die with 20 faces is marked with 20 letters of the alphabet (J, K, L, M, N and O are not included).

(i) The die is rolled twice. What is the probability that the same letter appears on each roll?

(ii) The die is rolled three times. What is the probability that the letter D appears exactly twice?

Answer.(i) Pr(same letter) = 1/20
(ii) Pr (D appears twice)
= 57/8,000.
  7. A game is played with two dice having the faces marked with 0, 1, 2, 3, 4 and 5. After throwing the dice, a score is calculated by multiplying the two numbers on the uppermost face together.

(i) What is the probability of obtaining a score of zero on the first turn?

(ii) What is the probability of scoring 16 or more on the first turn?

(iii) What is the probability that the sum of the scores in the first two turns is less that 45?

Answer.(i) Pr (zero) = 11/36.
(ii) Pr ≥ 16) = 1/9.
(iii) Pr (< 45) = 1291/1296.
  8.
   
  10.
   
Financial expectation.

Brett rolls a die. If he rolls a 6 he wins $10, but if he rolls an odd number he loses $1.

What is his financial expectation?

Answer.Expectation = 1/6 × 10 - 1/2 × 1
= $1.17.
   
   
  15.