# TSI Math: Adding Probabilities

A bag contains 12 grape candies, 7 apple candies, 10 strawberry candies, and 11 lemon candies. Nikki takes one candy from the bag, and then a second. What is the probability that she withdraws both an apple and a lemon candy, in either order?

Data Analysis, Statistics, and Probability | Probabilistic Reasoning |

Mathematics and Statistics Assessment | Probabilistic Reasoning |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Data Analysis, Statistics, and Probability |

TSI Mathematics | Data Analysis, Statistics, and Probability |

Test Prep | TSI |

### Transcript

okay nikki could either taken apple candy first and a

lemon candy second or a lemon candy first an apple

candy second right Either way probability and fruit candy make

a very fun paring right before nikki reaches into the

bag There are a total of twelve plus seven plus

ten plus eleven forty candies in the bag The probability

of taking an apple candy first is seven out of

forty because well seven out of the forty candies in

the bag or apple flavored Now there are only thirty

nine candies left in the bag so the probability gets

all wonky here Probability of taking one of the eleven

candies next is eleven out of thirty nine Well multiply

the individual probabilities together to find the total probability of

taking an apple candy first and a lemon candy seconds

We've got to calculate this whole thing first that seven

times eleven at seventy seven over whatever forty times thirty

nine years and the total there is point Oh for

nine force about five percent Okay great job so far

Using the same reasoning is before we find the probability

of taking a lemon candy first which is eleven Out

of forty all right we've removed one candy from the

bags of the probability of taking an apple candy Second

is seven out of thirty nine Well now he multiplied

those two probabilities together to find the total probability of

taking a lemon candy and then an apple candy and

we get eleven over forty times seven over thirty nine

And guess what It's still point Oh four nine four

Note that apple then lemon and lemon than apple have

the same probability Will the total probability of either one

of these two sequences of events occurring is the sum

of their probabilities We're goingto adam up so it's about

nine point eight percent They're rounded to match the answer

choices while the probability of taking both an apple and

a lemon candy then and either order is point Oh

nine nine yeah mingo nif isn't so that's it The 00:02:06.102 --> [endTime] answer is b and we're shmoop this