Test Index

Probability

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Question : 107 of 127

Marks: +1, -0

X

80\%

of the problems while

Y

90\%

of the problems given in a statistics book. A problem is selected at random. What is the probability that at least one of them will solve the problem.

0.95
0.98
0.96
0.99

Solution:

Concept:

Use complementary probability:

P(\text{at least one}) = 1 - P(\text{both fail})

, assuming independence.

Explanation:

X

solves

80\%

of problems, so

P(X\text{ solves}) = 0.8

, thus

P(X\text{ fails}) = 0.2

.

Y

solves

90\%

of problems, so

P(Y\text{ solves}) = 0.9

, thus

P(Y\text{ fails}) = 0.1

.

Probability both fail (neither solves)

= 0.2 \times 0.1 = 0.02

.

Therefore, probability at least one solves

= 1 - 0.02 = 0.98

.

Answer:

0.98

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