SAT Probability Question 56 | Free SAT Prep | Aniko

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Question 56·Medium·Probability and Conditional Probability

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A jar contains only blue, red, and green marbles, for a total of 180 marbles. A marble will be selected at random from the jar. The probability of selecting a blue marble is 0.35, and the probability of selecting a red marble is 0.40.

How many green marbles are in the jar?

For probability problems with a small number of categories that exhaust all possibilities, first use the fact that their probabilities must sum to 1 to find any missing probability. Then, to convert a probability into an actual count, multiply the probability by the total number of items or trials. On the SAT, write a quick equation like $p_1 + p_2 + p_3 = 1$ , solve for the unknown probability, and immediately multiply by the given total to save time and avoid unnecessary steps.

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Relate the three probabilities

The jar contains only blue, red, and green marbles. What must the sum of the probabilities of selecting blue, red, and green be?

Find the missing probability

You know the probabilities for blue and red marbles: $0.35$ and $0.40$ . Add them, then subtract that sum from 1 to find the probability of selecting a green marble.

Turn probability into a count

Once you know the probability of selecting a green marble, use the fact that probability = (number of favorable outcomes) ÷ (total number of outcomes) to find how many green marbles there are out of 180.

Desmos Guide

Compute the number of green marbles directly

In Desmos, type the expression 180*(1 - 0.35 - 0.40) and look at the value that Desmos outputs; this value is the number of green marbles in the jar.

Step-by-step Explanation

Use the fact that probabilities sum to 1

There are only blue, red, and green marbles, so the probabilities of selecting each color must add up to 1.

Let $P(G)$ be the probability of selecting a green marble. Then:

P(\text{blue}) + P(\text{red}) + P(G) = 1

You are given $P(\text{blue}) = 0.35$ and $P(\text{red}) = 0.40$ . Substitute these values into the equation.

Find the probability of selecting a green marble

Substitute the given probabilities into the equation:

0.35 + 0.40 + P(G) = 1

Add the known probabilities:

0.75 + P(G) = 1

Now subtract $0.75$ from both sides to solve for $P(G)$ :

P(G) = 1 - 0.75 = 0.25

So the probability of selecting a green marble is $0.25$ .

Convert the probability to a number of marbles

A probability of $0.25$ means that $25\%$ of the marbles are green.

To find the number of green marbles, multiply this probability by the total number of marbles (180):

\text{green marbles} = 0.25 \times 180

Compute the product:

0.25 \times 180 = 45

So there are 45 green marbles in the jar.

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Step-by-step Explanation

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Step-by-step Explanation