Brenda’s Bike Booth, at the mall, allows people to order a bike in their choice of 4 colors (Atomic Tangerine, Banana, Café Noir, or Dollar Bill) and the options of with or without a basket; with or without a horn. Given all of these options, what’s the probability that my daughter chooses either a banana colored bike with a basket, or an Atomic Tangerine colored bike without a horn?
*First part is the fundamental counting principle I believe = 16. But I am lost figuring out the probability! Thanks
The first part you have right fundamental counting principal = 4*2*2 = 16
Next we need to find out what are the chances she picks the banana colored bike with a basket = 2/16 or 1/8
and the chance she picks the Atomic Tangerine bike without the horn = 2/16 or 1/8
The key word in this question is OR. Chances of picking one bike OR the other. the formula of finding the probability of or = Probability(A)+P(B)-P(A&B)
Before we can do that we must find the Probability of (A&B)= 1/8*1/8=1/64
Now we can find the probability of OR = 1/8+1/8-1/64 = 15/64 or 0.234 which = 23.4%
To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Based on the given options, there are 4 colors to choose from and 2 options for the presence of a basket (with or without), as well as 2 options for the presence of a horn (with or without). Hence, there are a total of 4 x 2 x 2 = 16 possible outcomes.
Now let's determine the number of favorable outcomes.
For a banana-colored bike with a basket, there is only one option, as the question specifies that the bike must be banana-colored and with a basket.
For an Atomic Tangerine colored bike without a horn, again there is only one option, as the question specifies that the bike must be Atomic Tangerine colored and without a horn.
Therefore, the number of favorable outcomes is 1 + 1 = 2.
To find the probability, we simply divide the number of favorable outcomes by the total number of possible outcomes:
Probability = number of favorable outcomes / total number of possible outcomes
Probability = 2 / 16
Simplifying this fraction gives us the probability:
Probability = 1 / 8
So, the probability that your daughter chooses either a banana colored bike with a basket, or an Atomic Tangerine colored bike without a horn is 1 out of 8, or 1/8.