Hannah’s favorite toy character is sold wearing one of many outfits. An outfit consists of one shirt, one pair of pants, and one cap. The shirt can be striped, plain, or polka-dotted. The pants may be denim or plaid. The cap may be a cowboy hat or a baseball cap. If Hannah picks a toy at random from the shelf and there are an equal number of toys wearing each outfit, what is the probability that the toy is dressed in a polka-dotted shirt and a cowboy hat?
3 kind of shirts
2 kind of pants
2 kind of caps
number of possible outfits = 3*2*2 = 12
you have a choice of pants only, so there are 2 of those
so prob(of your event) = 2/12 = 1/6
To find the probability that the toy is dressed in a polka-dotted shirt and a cowboy hat, we first need to determine the total number of possible outfits.
Since there are three options for shirts (striped, plain, or polka-dotted), two options for pants (denim or plaid), and two options for caps (cowboy hat or baseball cap), the total number of possible outfits is:
3 options for shirts * 2 options for pants * 2 options for caps = 3 * 2 * 2 = 12 outfits
Now, let's determine the number of outfits that include a polka-dotted shirt and a cowboy hat. There is only 1 option for a polka-dotted shirt and 1 option for a cowboy hat, so the number of outfits with this combination is:
1 option for a polka-dotted shirt * 1 option for a cowboy hat = 1 * 1 = 1 outfit
Finally, we can calculate the probability by dividing the number of outfits with the desired combination by the total number of possible outfits:
Probability = Number of outfits with polka-dotted shirt and cowboy hat / Total number of possible outfits
Probability = 1 outfit / 12 outfits
Therefore, the probability that the toy is dressed in a polka-dotted shirt and a cowboy hat is 1/12.