# ACT Aspire Math: Multiplying a Sequence of Probabilities

Lena's sock drawer contains 10 pairs of socks. There is a spider living in one of these pairs of socks.

If Lena randomly takes two pairs of socks from the drawer, what is the probability that both pairs are spider-free?

ACT Aspire | Math |

ACT Aspire Math | Statistics & Probability |

Math | Statistics & Probability |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

event is the ratio of desired outcomes Two possible outcomes

right desired over possible Our personal desired outcome would be

zero spiders taking up residence in our sock drawer but

well lena's a live and let spider live type of

gal Start with the first pair of socks There are

nine desired outcomes and you know pairs of socks with

no spider and ten possible outcomes She could pick any

of the ten pairs of socks right None of restricted

So there's a nine in ten chance that the first

pair has no spider Well now that she's picked the

first pair of socks there are nine pairs left and

eight of these nine pairs don't have the spider The

probability that she picks one of these is eight over

nine Well these air too dependent events because the probability

of picking the sock with the spider on the second

draw changes after the first selection right The denominator shrinks

the formula for calculating the probability of two dependent events

lp of times p f b once a has occurred

is pf and be well to find the probability that

both bears are spider free Apply this formula to the

two probabilities and we get nine tense times eight nine

switches seventy two over ninety which is same as eight

over ten or eighty percent So yeah those air Fairly

decent odds They're not decent enough to keep us from

checking our socks for spiders though forever and ever but 00:01:42.872 --> [endTime] well they're decent enough No