Probability Practice Test 2

Question : 19 of 37

Marks: +1, -0

You enter a chess tournament where your probability of winning a game is 0.3 against half the players (call them Type 1), 0.4 against a quarter of the players (call them Type 2), and 0.5 against the remaining quarter of the players (call them Type 3). You play a game against a randomly chosen opponent. What is the probability of winning the tournament?

0.365
0.452
0.375
0.236

Validate

Solution:

Let

A_i

be the event of playing with an opponent of type

P(A_1) = 0.5

P(A_2) = 0.25

P(A_3) = 0.25

,
Let B be the event of winning

P(B/A_1) = 0.3

P(B/A_2) = 0.4

P(B/A_3) = 0.5

,
Thus by total probability theorem, probability of winning is:
P(B) = 0.5 × 0.3 + 0.25 × 0.4 + 0.25 × 0.5 = 0.375

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