Second fruit e Orange First fruit A bowl contains 12 pieces of fruit. There are

Question

Second fruit e Orange First fruit A bowl contains 12 pieces of fruit. There are four oranges and the remainder are apples. A piece of fruit is taken at random from the bowl and eaten. A second piece of fruit is then taken at random from 8. Orange Apple the bowl. Orange The tree diagram shows all the ways in which two pieces of fruit can be taken from the bowl. Copy the diagram and write the probabilities on it. ( Apple Apple (i) Use your tree diagram to calculate the probability that (a) One piece of fruit is an orange and the other is an apple (b) Both pieces are an apple (c) Both pieces are an orange In a lottery, 28 numbered balls are used. Seven of the balls are red. i) A ball is drawn at random and replaced. Then a second ball is drawn. Find the 9. probability that (a) The first is red (b) Both are red (c) The first is red and the second is not red (d) One is red and the other is not red (ii) If the first ball drawn is not replaced, find the probability that: (a) Both are red (b) One is red and the other not red, in anv orde

Explanation / Answer

Question 8:

(i) Here there are 4 cases given in the decision tree. The probabilities of each are computed as:

(ii) a) Probability that one piece of fruit is apple and another is orange is computed as:

= Probability that first is apple and second is orange + Probability that first is orange and second is Apple

= 0.2424 + 0.2424 = 0.4848

b) Probability that both pieces are apples = 0.4242 ( already computed in previous part )

c) Probability that both pieces are oranges = 0.0909 ( already computed in previous part )

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