suppose-that-the-probability-that-a-randomly-selected-employees-security-badge-s

Question

Suppose that the probability that a randomly selected employee's security badge scan fails at the entrance is $0.074$ . A company’s system checks badge scans in groups of $5$ employees. The system flags the group only if at least one scan fails. Find the probability that the group of $5$ employees will trigger a flag due to at least one badge failure. Should the company prepare for frequent individual re-checks?

Accepted Answer

$0.319$ — Re-checks are likely to be needed quite often.

Answer

$0.319$ — Most groups will fail the scan and require further checks.

Answer

$0.319$ — Re-checks will almost never be needed for any group.

Answer

$0.319$ — Nearly half of the groups will be automatically cleared.