Statistics: Probability

Question

A person is selected at random during the Republican National Convention. Suppose the probability that the person selected is a woman is 36%, the probability that the person selected is tall is 51%, and the probability that the person selected is left-handed is 12%.

Assume that being female, tall, and left-handed are independent of each other.

What is the probability that the person selected is a tall, left-handed woman?

Answer 1

Hi Briana,

Since the three are independent the answer is simply the product of the three probabilities 0.36*0.51*0.12 = 0.022032 or 2.2%

If you want an intuitive understanding of this, imagine that there are a total of 1000 people. The number of females would then be 360 (36% of 1000). Of the 360 females, about 184 would be tall (51% of 360). Of the 184 tall females, 22 (12% of 184) would be left handed. So there would be 22 females who are tall and left-handed. This implies a probability of 22/1000 = 0.022.

Regards,

Sujith