In a net session, Ravi hits the stumps with probability 3/5 and Kiran with probability 1/4, independently. Each bowls one ball. Find the probability that (i) the stumps are hit, (ii) exactly one of them hits.

1. 1 · Write what is given and what is to be found. Let R: Ravi hits, K: Kiran hits. P(R) = 3/5, P(K) = 1/4, and R and K are independent.
2. 2 · Write the rule. For independent events, P(R ∩ K) = P(R) · P(K); their complements are also independent.
3. 3 · Work out (i).
   • P(neither hits) = P(R′) · P(K′) = (2/5)(3/4) = 6/20 = 3/10
   • P(stumps hit) = 1 − 3/10 = 7/10
4. 4 · Work out (ii).
   • Only Ravi: (3/5)(3/4) = 9/20
   • Only Kiran: (2/5)(1/4) = 2/20
   • P(exactly one) = 9/20 + 2/20 = 11/20
5. 5 · Say what it means. With these two bowlers, the stumps fall on about 7 out of 10 such turns.
6. 6 · Check and box the answer. P(both) = 3/20, and 3/20 + 11/20 + 6/20 = 1. (i) 7/10 (ii) 11/20.

Scoring tip: For 'at least one', use 1 − P(none). It is shorter and safer than adding cases.