The chances for passing an endurance test for three threshers P, Q and R are 1/6, 1/4, and 1/2, respectively. The probability of passing the endurance test by at least one thresher, in fraction, is __________. (Rounded off to 2 decimal places)
Official Answer Key:
0.68 to 0.69
Step-by-Step Solution & Explanation
For independent events, “at least one” is most easily handled through the complement:
P(at least one passes) = 1 − P(none passes)
Step 1 — probability each fails:
P(P fails) = 1 − 1/6 = 5/6
P(Q fails) = 1 − 1/4 = 3/4
P(R fails) = 1 − 1/2 = 1/2
Step 2 — all three fail (independent):
(5/6) × (3/4) × (1/2) = 15/48 = 0.3125
Step 3 — at least one passes:
1 − 0.3125 = 0.6875 = 0.69
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