There are m fruits in a basket. 3 of the fruits are kiwis; the rest are lemons. The probability of picking two kiwis in a row (without replacement) is 0.3. Show m^2 - m - 20 = 0.

Number of lemons = m - 3. Construct a tree diagram using the information given to represent picking two fruits out of the basket (without replacement) one after the other. Since picking each fruit is an independent event, just multiply probabilities to find the probability of selecting a kiwifruit twice in a row: P(two kiwifruits in a row) = 3/m * 2/(m - 1) and set this equal to 0.3 (given in the question). A bit of rearrangement of the algebra gives: 3/10 = 6/[m(m - 1)] => 3m(m - 1) = 60 => m(m - 1) = 20 => m² - m - 20 = 0 as required.