Competency Practice

Two-dice sum combinations, 3-coin games, deck removals, numbered discs, and geometric probability.

Answer all questions.

Show all necessary working.

Use a separate notebook for your solutions.

Two distinguishable fair dice are rolled. Find the probability that their sum is 7, and explain why the eleven possible sums are not equally likely.
Three fair coins are tossed. A player wins when all three show the same face. Find the probability that the player loses.
Five cards labelled 10, J, Q, K, A are shuffled. Find $P(Q)$ on the first draw. If Q is removed, find $P(A)$ and $P(Q)$ on the second draw.
A box contains discs numbered 1 to 90. Find the probabilities of drawing a two-digit number, a perfect square, and a multiple of 5.
A lot contains 132 good pens and 12 defective pens. Find the probability that a randomly selected pen is good.
A point is chosen uniformly in a $3\text{ m}\times2\text{ m}$ rectangle. Find the probability that it lies inside a circle of diameter 1 m wholly inside the rectangle.

Neokaal Study

Answer Key

$6/36=1/6$; the sums have different numbers of ordered pairs
1. Write the ordered sample space or count it systematically.
2. Count favourable outcomes, divide by the total, and use complements where helpful.
$6/8=3/4$
1. Write the ordered sample space or count it systematically.
2. Count favourable outcomes, divide by the total, and use complements where helpful.
$1/5, 1/4,$ and $0$
1. Write the ordered sample space or count it systematically.
2. Count favourable outcomes, divide by the total, and use complements where helpful.
$9/10, 1/10,$ and $1/5$
1. List or count the equally likely elementary outcomes.
2. Divide favourable outcomes by total outcomes and simplify.
$11/12$
1. Complementary probabilities add to 1.
2. Count one event directly and subtract from 1 when that is shorter.
$\pi/24$
1. List or count the equally likely elementary outcomes.
2. Divide favourable outcomes by total outcomes and simplify.