Final Answer:
The closest option is 0.25, but the correct probability is approximately 0.02, the correct answer is not provided among the options (A) 0.25, (B) 0.50, (C) 0.75, or (D) 1.00.
Step-by-step explanation:
Let's break down the problem step by step.
1. Probability of the first bag being chosen:
The problem states that each bag has a 14% chance of being selected. The probability of the first bag being chosen is 0.14.
2. Probability of the second bag being chosen:
The bags are chosen independently, meaning the selection of one bag does not affect the probability of the other being chosen. Therefore, the probability of the second bag being chosen is also 0.14.
3. Probability of both bags being chosen:
Since the events are independent, you find the probability of both events happening by multiplying the individual probabilities.
[P{both bags chosen} = P{first bag chosen} x P{second bag chosen}]
[P{both bags chosen} = 0.14 x 0.14
[P{both bags chosen} = 0.0196 ]
So, the probability that both bags are selected for extra screening is 0.0196.
4. Rounding to two decimal places:
The question asks to round the probability to two decimal places. So, rounding 0.0196 to two decimal places gives approximately 0.02.
Therefore, the correct answer is not provided among the options (A) 0.25, (B) 0.50, (C) 0.75, or (D) 1.00. The closest option is 0.25, but the correct probability is approximately 0.02.
Complete question:
At an airport, bags are randomly chosen for extra security screening. Each bag has a 14% chance of being selected. It doesn't matter if one bag is chosen or not, it doesn't affect the chance of another bag being chosen. If two bags go through the system, we want to know the chance that both bags are chosen. We need to find the probability and round it to two decimal places.
What is the probability that both bags are selected for extra screening?
A) 0.25
B) 0.50
C) 0.75
D) 1.00