# Probability

## 2009 May June Paper 6/1-Q5

At a zoo, rides are offered on elephants, camels and jungle tractors. Ravi has money for only one ride. To decide which ride to choose, he tosses a fair coin twice. If he gets 2 heads he will go on the elephant ride, if he gets 2 tails he will go on the camel ride and if he gets 1 of each he will go on the jungle tractor ride.
(i) Find the probabilities that he goes on each of the three rides. 

$$\mathrm{P}(\mathrm{E})=1 / 4, \mathrm{P}(\mathrm{C})=1 / 4, \mathrm{P}(\mathrm{JT})=1 / 2$$

The probabilities that Ravi is frightened on each of the rides are as follows: elephant ride $$\frac{6}{10}$$, camel ride $$\frac{7}{10}$$, jungle tractor ride $$\frac{8}{10^{\circ}}$$.
(ii) Draw a fully labelled tree diagram showing the rides that Ravi could take and whether or not he is frightened. Ravi goes on a ride.
(iii) Find the probability that he is frightened. 

$$\mathrm{P}(\mathrm{F})=(1 / 4 \times 6 / 10)+(1 / 4 \times 7 / 10)+$$ $$(1 / 2 \times 8 / 10)$$
$$=29 / 40(0.725)$$

(iv) Given that Ravi is not frightened, find the probability that he went on the camel ride. 

$$\mathrm{P}(C \mid N F)=\frac{P(C \cap N F)}{P(N F)}$$
$=\frac{3 / 40}{(1-29 / 40)}$
$=3 / 11(0.273)$
OR using ratios $$3 /(4+3+4)$$