Question

A new drug on the market is known to cure 30% of patients with cervical cancer. If a group of 18 patients is randomly selected, what is the probability of observing, at most, one patient who will be cured of cervical cancer?

a) ( 18/1 choose 1(0.30)¹(0.70)¹⁷ )

b) ( 1 - 18/1 choose 1(0.30)¹(0.70)¹⁷ )

c) ( 18/0 choose 0(0.70)¹⁸ )

d) ( 1 - 18/0 choose 0(0.70)¹⁸ )

e) ( 18/0 choose 0(0.70)¹⁸ + 18/1 choose 1(0.30)¹(0.70)¹⁷ )

Answer 1

The correct answer is option e, reflecting the binomial probability of at most one cured patient out of 18, which is the sum of the probabilities of observing 0 and 1 cures.

Step-by-step explanation:

The question deals with a scenario involving binomial probability. We are given the probability of success (curing a patient with cervical cancer) as 30% or 0.30, and we are looking for the probability of observing at most one success in a trial of 18 patients.

To calculate this, we need to sum the probabilities of 0 successes and 1 success:

• For 0 successes: (18 choose 0) × (0.30)0 × (0.70)18
• For 1 success: (18 choose 1) × (0.30)1 × (0.70)17

Combining these two probabilities gives us the final answer:

( 18/0 choose 0(0.70)18 + 18/1 choose 1(0.30)1(0.70)17 )

This corresponds to option e. Thus, the correct answer is option e, which is the sum of the probabilities of observing 0 cured patients and 1 cured patient among the 18 patients. The use of binomial coefficients and the binomial probability formula is crucial for this calculation.