Grade 7 · Statistics & probability

Two-event compound probability word problems practice

Two-event compound probability word problems is a grade 7 math skill aligned to Common Core standard 7.SP.C.8: find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 two-event compound probability word problems problems our math games drill.

CCSS 7.SP.C.810 questions in the bank
Sample questions

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Question 1easy

Two fair coins are flipped. What is the probability that both coins show heads?

P(heads on one coin)=12P(\text{heads on one coin}) = \dfrac{1}{2}. For two independent flips, P(both heads)=12×12=14P(\text{both heads}) = \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}.

Question 2easy

A game spinner has 88 equal sections, exactly 22 of which are blue. A fair coin is then flipped. What is the probability of landing on blue on the spinner and getting tails on the coin?

P(blue)=28=14P(\text{blue}) = \dfrac{2}{8} = \dfrac{1}{4} and P(tails)=12P(\text{tails}) = \dfrac{1}{2}. So P(both)=14×12=18P(\text{both}) = \dfrac{1}{4} \times \dfrac{1}{2} = \dfrac{1}{8}.

Question 3easy

A standard six-sided number cube is rolled twice. What is the probability of rolling a 22 both times?

P(2 on one roll)=16P(2\text{ on one roll}) = \dfrac{1}{6}. For two independent rolls, P(both 2s)=16×16=136P(\text{both }2\text{s}) = \dfrac{1}{6} \times \dfrac{1}{6} = \dfrac{1}{36}.

Question 4easy

The weather report says there is a 35\dfrac{3}{5} chance of no rain on Saturday and an independent 35\dfrac{3}{5} chance of no rain on Sunday. What is the probability that it does not rain on both days?

Multiply the independent probabilities: 35×35=925\dfrac{3}{5} \times \dfrac{3}{5} = \dfrac{9}{25}.

Question 5easy

Spinner A has 55 equal sections and exactly 11 section is gold. Spinner B has 44 equal sections and exactly 11 section is gold. Each spinner is spun once. What is the probability that both spinners land on gold?

P(gold on A)=15P(\text{gold on A}) = \dfrac{1}{5} and P(gold on B)=14P(\text{gold on B}) = \dfrac{1}{4}. So P(both gold)=15×14=120P(\text{both gold}) = \dfrac{1}{5} \times \dfrac{1}{4} = \dfrac{1}{20}.

Question 6medium

A standard six-sided number cube is rolled twice. What is the probability of rolling a 44 on the first roll and an even number on the second roll?

P(4 on first roll)=16P(4\text{ on first roll}) = \dfrac{1}{6} and P(even on second roll)=36=12P(\text{even on second roll}) = \dfrac{3}{6} = \dfrac{1}{2}. So P(both)=16×12=112P(\text{both}) = \dfrac{1}{6} \times \dfrac{1}{2} = \dfrac{1}{12}.

Question 7medium

A bag contains 44 red marbles and 66 blue marbles. One marble is drawn at random, its color is recorded, and it is placed back in the bag. A second marble is then drawn at random. What is the probability that both marbles are red?

With replacement, each draw is independent: P(red)=410=25P(\text{red}) = \dfrac{4}{10} = \dfrac{2}{5}. So P(both red)=25×25=425P(\text{both red}) = \dfrac{2}{5} \times \dfrac{2}{5} = \dfrac{4}{25}.

Question 8medium

A game spinner has 66 equal sections numbered 11 through 66. The spinner is spun twice. What is the probability that both spins land on a number greater than 44?

P(greater than 4)=26=13P(\text{greater than }4) = \dfrac{2}{6} = \dfrac{1}{3} on each spin. The spins are independent, so P(both)=13×13=19P(\text{both}) = \dfrac{1}{3} \times \dfrac{1}{3} = \dfrac{1}{9}.

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Blaster Gate gameBlaster GateBlast through the wall. First to clear wins.Blitz Tanks gameBlitz TanksSolve math to load shells. Out-think the battalion. Last math standing wins.
Tests that cover two-event compound probability word problems:
NAEPPSAT 8/9SBACSC READYNC EOG/EOC
More Grade 7 skills:
Sampling and inferenceSimple interestTwo-event conditional probability word problemsProbability of simple eventsRatios, rates, and proportionsProbability basicsRatio, rate, and proportion word problemsVolume of prisms and cylindersAll Grade 7 practice →

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