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1983 AMC 12 Question 26

AMC12 · 1983 AMC 12

Question 26

The probability that event $A$ occurs is $\frac34;$ the probability that event $B$ occurs is $\frac23.$ Let $p$ be the probability that both $A$ and $B$ occur. The smallest interval necessarily containing $p$ is the interval
  1. $[\frac1{12},\frac12]$
  2. $[\frac5{12},\frac12]$
  3. $[\frac12,\frac23]$
  4. $[\frac5{12},\frac23]$
  5. $[\frac1{12},\frac23]$