Question

the probability of picking a white ball from a bag is 0.3. the probability of not picking a red ball from the bag is twice the probability of picking a white ball. what is the probability of picking a red ball?

Explanation:

Step1: Find the probability of not picking a red ball

Given that the probability of picking a white ball \(P(W)=0.3\). The probability of not picking a red ball \(P(\text{not }R)\) is twice the probability of picking a white ball. So \(P(\text{not }R) = 2\times P(W)\)
\(P(\text{not }R)=2\times0.3 = 0.6\)

Step2: Use the formula \(P(R)=1 - P(\text{not }R)\)

The formula for the probability of an event \(R\) (picking a red ball) and its complement (\(\text{not }R\), not picking a red ball) is \(P(R)+P(\text{not }R)=1\). Rearranging for \(P(R)\), we get \(P(R)=1 - P(\text{not }R)\)
Substitute \(P(\text{not }R) = 0.6\) into the formula: \(P(R)=1- 0.6\)

Answer:

\(0.4\)