Difficulty: Easy

Average Score: 100%

Janine kept a record, shown in the table above, of how often she stopped for a red light at each of the 4 traffic signals on the road she travels to work each day. Assume that the traffic signals operate independently of each other and the given percentages accurately reflect her future stopping percentages.

If Janine obeys all traffic laws, what is the probability, to the nearest percent, that Janine will stop only at Intersections B and C and not at Intersections A and D on her way to work on any given day?

Rationale

The probability that Janine will stop only at Intersections B and C and not at Intersections A and D is 4%.

To find this probability, we multiply the probabilities of stopping at Intersections B and C together and then multiply that by the probabilities of not stopping at Intersections A and D. The calculations yield a combined probability of 4%.

A (2%) YOUR ANSWER

This option underestimates the likelihood of Janine stopping at both B and C, while still accounting for the correct non-stopping probabilities at A and D. The calculations suggest that the combined probabilities yield a higher percentage than 2%.

B (4%) CORRECT

This is the correct choice. The calculation involves multiplying the individual probabilities of stopping at B and C (which are higher) and those of not stopping at A and D (which are lower). This combination results in a total of 4%, accurately reflecting Janine's stopping behavior.

C (12%) YOUR ANSWER

This choice suggests a higher probability than calculated. It likely results from miscalculating the probabilities of stopping or not stopping at the intersections, mistakenly assuming a higher chance of stopping at A or D.

D (42%) YOUR ANSWER

This option greatly overestimates the likelihood of stopping at B and C while disregarding the probabilities of not stopping at A and D. Such a high value does not align with the calculated probabilities based on the provided data.

E (70%) YOUR ANSWER

This choice is inaccurate as it assumes a very high probability of stopping at both B and C without properly accounting for the probabilities of not stopping at A and D. The combination of stopping and not stopping should lead to a significantly lower percentage.

Conclusion

In summary, the correct probability that Janine will stop only at Intersections B and C and not at Intersections A and D is 4%. This result is derived from correctly applying the probabilities of stopping and not stopping at each intersection, reflecting the independent nature of traffic signals on her route. Understanding these probabilities is crucial for accurately predicting Janine's behavior at traffic signals.

If Janine obeys all traffic laws, what is the probability, to the nearest percent, that Janine will stop only at Intersections B and C and not at Intersections A and D on her way to work on any given day?

The probability that Janine will stop only at Intersections B and C and not at Intersections A and D is 4%.

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