Question 1. [6 Marks] Two cold tablets are accidentally places in a box containi

Question

Question 1. [6 Marks] Two cold tablets are accidentally places in a box containing three aspirin tablets. The five tablets are identical in appearance. One tablet is selected at random from the box and is swallowed by the first patient. A tablet is then selected at random from the four remaining tablets and is swallowed by the second patient. a) 1 mark] Write out the sample space b) Determine the probability that i) [I mark the first patient obtained a cold tablet i) [1 mark] the second patient obtained a cold tablet. i 1 mark] neither patients obtained a cold tablet iv) mark] either the first or second patient obtained a cold tablet. v) 1 mark only one of the patients obtained a cold tablet.

Explanation / Answer

let event cold and aspirin tablet taken is represented by C and A

a) sample space ={ CC ,AA ,CA ,AC}

b)

i)P(first patient obtained a cold tablet) =2/5 (as there are 2 cold talets out of 5)

ii)P(second patient obtained a cold tablet)=P(first takes aspirin and second cold)+P(both first and second take out cold tablet)=(3/5)*(2/4)+(2/5)*(1/4)=2/5

iii)P(neither ontained a cold tablet)=P(both takes aspirin)=(3/5)*(2/4)=3/10

iv)P(either first or second obtained a cold tablet)=1-P(neither ontained a cold tablet)=1-3/10=7/10

v)P(only one takes cold tablet)=P(first takes aspirin and second cold)+P(first takes cold and second aspirin)=(3/5)*(2/4)+(2/5)*(3/4)=3/5

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