Question

In the following probability distribution, the value of p is:

• A. \( \frac{7}{40} \)
• B. \( \frac{1}{10} \)
• C. \( \frac{9}{35} \)
• D. \( \frac{1}{4} \)

Hint:

The fundamental property of any probability distribution is that the sum of the probabilities of all possible values of the random variable must equal 1. Use this property to set up an equation and solve for any unknown probabilities or parameters in the distribution.

Answer 1

The Correct Option is A

For a probability distribution, the sum of the probabilities of all possible outcomes must be equal to 1. In this case, the possible values of X are 0, 1, 2, and 3, and their corresponding probabilities are \( P(X=0) = p \), \( P(X=1) = p \), \( P(X=2) = 0.3 \), and \( P(X=3) = 2p \). Therefore, we have the equation: $$ P(X=0) + P(X=1) + P(X=2) + P(X=3) = 1 $$ $$ p + p + 0.3 + 2p = 1 $$ Combine the terms with \( p \): $$ 4p + 0.3 = 1 $$ Subtract \( 0.3 \) from both sides: $$ 4p = 1 - 0.3 $$ $$ 4p = 0.7 $$ Now, solve for \( p \): $$ p = \frac{0.7}{4} = \frac{7/10}{4} = \frac{7}{10 \times 4} = \frac{7}{40} $$ So, the value of \( p \) is \( \frac{7}{40} \).