Topic 4.5: Probability Fundamentals Questions

Items from a machine are faulty with probability 0.03. In a day it makes 1500 items. Find the expected number of faulty items.

A spinner has 5 equal sectors: 2 blue, 2 red, 1 yellow. It is spun 60 times. Find the expected number of yellows.

Two fair coins are tossed. List the sample space and find the probability of exactly one head.

A spinner has 8 equal sectors numbered 1–8. It is spun once.

The probability a seed germinates is 0.85. A gardener plants 200 seeds. Find the expected number that germinate.

A bag has 3 red and 9 green balls. One is drawn, its colour noted, and replaced; this is repeated 48 times. Find the expected number of reds.

The probability a bus is late on a given day is 0.15. Over a 40-day period:

A bag contains 6 red, 4 yellow and 2 green sweets. One is chosen at random.

A box holds $4$ keys, and exactly one of them opens a lock. Keys are tried one at a time, in a random order, and a key that fails is put aside. Let $X$ be the number of keys tried, up to and including the one that opens the lock.

Explain why $X\le 4$.

The probability that a light bulb fails within a year is $0.04$. A hotel fits 750 of these bulbs. Find the expected number that fail within a year.

A fair six-sided die is rolled 240 times. Find the expected number of sixes.

Show that $P(\text{red})=\frac{5}{12}$.

In a class of 30 students, 12 study art and the rest do not. A student is chosen at random. Find the probability the student does not study art.

Write down $P(A^{\prime })$.

Explain why this answer must be wrong.

A bag contains counters that are green, red or blue. There are exactly 8 green counters, and the number of red counters equals the number of blue counters. A counter is taken at random from the bag. The probability that it is green is 0.25.

Show that there are 12 red counters in the bag.

A bag contains counters that are yellow, red or blue. There are exactly 18 yellow counters, and the number of red counters equals the number of blue counters. A counter is taken at random from the bag. The probability that it is yellow is 0.3.

Show that there are 21 red counters in the bag.

A pack of $10$ cards contains $3$ red cards and $7$ black cards. Cards are drawn one at a time, without replacement, until a black card is drawn. Let $N$ be the number of cards drawn. Explain why $N\le 4$.

The probability that a spinner lands on blue is $k$. Using the results of a game, a student forms the equation $10k^2-17k+3=0$, which has solutions $k=0.2$ and $k=1.5$. State why $k=0.2$ is the only valid solution.

Three fair coins are tossed 96 times. Find the expected number of times all three land heads.