Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have red logo jerseys. Five teams of Pool-B have blue logo jerseys while the rest three have red logo jerseys.
If one team from each pool reaches the final, the probability that one team has a blue logo jersey and another has a red logo jersey is ________ (rounded off to one decimal place).
ANSWER
The probability that one finalist has a blue logo jersey and the other a red one is .
Official answer: 0.5Source: Official answer key, GATE 2024 IN (IISc Bengaluru)
Each pool has teams. Pool-A has 4 blue and 4 red; Pool-B has 5 blue and 3 red. Each team in a pool is taken to be equally likely to be that pool's finalist, and the two pools are independent.
Probabilities within each pool (subscript = blue, = red): , , , .
"One blue and one red" happens in exactly two ways that cannot both occur: (Pool-A blue and Pool-B red) or (Pool-A red and Pool-B blue).
Multiply for each independent pair, then add the two exclusive cases:
. Check with the complement: (both blue plus both red), so .
KEY IDEA
The two finalists come from different pools, so the events are independent. Split "one blue, one red" into its two exclusive cases (A blue with B red, and A red with B blue), multiply within each case and add the two. Checking with the complement (both the same colour) confirms the result.
WATCH OUT FOR
Counting only one case (for example A blue, B red ) and forgetting the reverse case. Another mistake is pooling all 16 teams and using or . That ignores the fact that exactly one finalist comes from each pool.
From the GATE 2024 IN paper. Every question of this paper · Download the full paper · All 33 Probability & statistics questions, with notes
