9) A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim, each purchased one gumball. What is the likelihood both Sue and Jim get red gumballs
0.062
Probability of both/events occurring is found by multiplying the probabilities of the individual events.
Note that after Sue picks a red gumball, there are one less red and one less total gumballs for Jim.
(100/400)(99/399) = ?
To find the likelihood (probability) that both Sue and Jim get red gumballs, we need to determine the probability of Sue getting a red gumball and then multiply that by the probability of Jim also getting a red gumball.
First, let's find the probability of Sue getting a red gumball.
There are a total of 400 gum balls in the machine (50 black + 150 white + 100 red + 100 yellow = 400).
Out of these, there are 100 red gumballs.
Therefore, the probability of Sue getting a red gumball is 100/400, which simplifies to 1/4 or 0.25.
Next, let's find the probability of Jim getting a red gumball.
Since Sue has already taken a gumball, there are now 399 gum balls left in the machine.
Out of these, there are 99 red gumballs remaining (since Sue took one red gumball).
So, the probability of Jim getting a red gumball is 99/399, which simplifies to 11/39 or approximately 0.28.
To find the probability that both Sue and Jim get red gumballs, we multiply their individual probabilities together:
Probability (both Sue and Jim get red gumballs) = Probability(Sue gets red) * Probability(Jim gets red)
= 0.25 * 0.28
≈ 0.07
Therefore, the likelihood (probability) that both Sue and Jim get red gumballs is approximately 0.07 or 7%.