Sure, let's go through each part of the question step-by-step:
### Part a)
What is the probability of a side effect when using the new medicine? Give your answer in standard form.
First, we are given that the probability of a side effect with the old medicine is [tex]\( 2 \times 10^{-6} \)[/tex].
Since the new medicine is 50% more likely to cause a side effect, we need to calculate a 50% increase in the probability.
1. Determine the increase factor due to the new medicine:
- A 50% increase means an increase factor of [tex]\( 1 + \frac{50}{100} = 1.5 \)[/tex].
2. Calculate the new probability:
- New probability = [tex]\( \text{Old probability} \times \text{Increase factor} \)[/tex]
- New probability = [tex]\( 2 \times 10^{-6} \times 1.5 \)[/tex]
3. Perform the multiplication:
- New probability = [tex]\( 3 \times 10^{-6} \)[/tex]
Thus, the probability of a side effect when using the new medicine, in standard form, is [tex]\( 3 \times 10^{-6} \)[/tex].
### Part b)
Write your answer to part a) as an ordinary number.
The standard form of the new probability is [tex]\( 3 \times 10^{-6} \)[/tex]. To convert this to an ordinary number:
[tex]\[
3 \times 10^{-6} = 0.000003
\][/tex]
Thus, the probability of a side effect with the new medicine is [tex]\( 0.000003 \)[/tex] as an ordinary number.
### Part c)
Write a sentence to explain whether you would be concerned about the increase in the probability of a side effect when using the new medicine.
Considering that the original probability of a side effect with the old medicine was [tex]\( 2 \times 10^{-6} \)[/tex] and the new probability is [tex]\( 3 \times 10^{-6} \)[/tex]:
Despite the increase by 50%, the overall probability of a side effect remains very low. Thus, the increase in the probability of a side effect is very small, so there is little cause for concern.
