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Chapter 39: Q 1 Exercise (page 1136)

An experiment has four possible outcomes, labeled A to D. The probability of A is P_A= 40% and of B is P_B = 30%. Outcome C is twice as probable as outcome D. What are the probabilities P_Cand P_D?

Short Answer

Expert verified

Therefore the probabilities are:

$P_{D} = 0.1 P_{C} = 0.2$

Step by step solution

01

Given information

An experiment has four possible outcomes, labeled A to D. The probability of A is P_A= 40% and of B is P_B = 30%. Outcome C is twice as probable as outcome D.

02

Explanation

The most crucial principle in this problem is that all conceivable outcomes' probability must add up to 1, or 100%. As a result, utilising the information provided in the problem, we can develop two equations.

$P_{C} = 2 P_{D} (1) P_{A} + P_{B} + P_{C} + P_{D} = 1 0.40 + 0.30 + P_{C} + P_{D} = 1 P_{C} + P_{D} = 0.3 (2)$

Solving (1) with (2)

role="math" localid="1648583743410" $3 P_{D} = 0.3 P_{D} = 0.1 P_{C} = 0.2$

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