A medical device company knows that 11 percent of patients experience injection-site reactions with the current needle. If 4 people receive injections with this type of needle, what is the probability that none of the 4 people get an injection-site reaction?

If 11% of patients have a reaction, the probability of no reaction is 1 − 0.11 = 0.89. Assuming the four patients’ outcomes are independent, the probability that none reacts is 0.89⁴ = 0.6274, so the answer is 0.6274.

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