Discrete probability distributions

Below is a probability table for the for the throw of a single dice.

(a) Find the value of t
(b) What is the probability of throwing less than a five?

Probabilities must sum to 1, so

\[ \begin{align} 1 &= 1 -5t + t + 1-5t + t + 1-5t + t \\ 1 & = 3 - 12t \\ 12t &= 2 \\ t = \frac{1}{6} \end{align} \ \]

Subtract the probabilities for five and six from 1.

\[ \begin{align} P(X \le 4) &= 1 - (P(X = 5) + P(X = 6)) \\ &= 1 - (2/6) \\ &= 4/6 \end{align} \ \]

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

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Now You Try:

Above is a probability table.

(a) Find the value of t
(b) What is the probability of (X < 3)?