Discrete random variables and distribution tables Problem set A

A biased coin lands heads with probability 0.7. It is tossed twice. X is the number of heads.

1. (a) Write the probability distribution of X as a table.
2. (b) Find P(X ≥ 1).

A fair 10-sided die has faces numbered 1 to 10. It is rolled once and X is the number shown.

1. (a) Write down P(X = x) for each score.
2. (b) Find P(X ≥ 8).
3. (c) Find P(3 ≤ X ≤ 6).

The table shows the probability distribution of X, the number of cars owned by a household.

1. (a) Find the value of k.
2. (b) Find P(X ≤ 1).
3. (c) Find P(X ≥ 3).

The probability that Sam cycles to school on any one day is 0.6. The days are independent. X is the number of days he cycles in a three-day school week.

1. (a) Write the probability distribution of X as a table.
2. (b) Find P(X ≥ 2).

A bag holds 5 red counters and 4 white counters. Two counters are taken at random without replacement. X is the number of red counters taken.

1. (a) Write the probability distribution of X as a table.
2. (b) Find P(X ≥ 1).

A fair four-sided die has faces numbered 1 to 4. It is rolled three times and X is the number of times a 3 is rolled.

1. (a) Write the probability distribution of X as a table.
2. (b) Find P(X ≥ 1).

The table shows the probability distribution of G, the number of goals a team scores in a match.

1. (a) Find the value of k.
2. (b) Find P(G ≥ 2).
3. (c) Find P(G ≥ 3 | G ≥ 2).

A discrete random variable X has the distribution shown, where k is a constant.

1. (a) Show that k² + 3k − 0.64 = 0.
2. (b) Use your calculator to solve this equation and state the value of k.
3. (c) Find P(X ≥ 3).

A box holds 4 red pencils and 3 blue pencils. Three pencils are taken at random without replacement. X is the number of red pencils taken.

1. (a) Write the probability distribution of X as a table.
2. (b) Find P(X ≥ 1).
3. (c) Find P(X = 2 | X ≥ 1).