Question

1. (2 pts)The probability that Sue will go to Mexico in the winter and to France in the summer is 0.40. The probability that she will go to Mexico in the winter is 0.60. Find the probability that she will go to France this summer given that she just returned from her winter vacation in Mexico.

2. (2 pts ) A fair die is tossed. Find the probability P(less than 5|even).

3. ( 2 pts) You have decided to take a vacation. You want to go from Los Angeles to San Francisco and then to Hawaii, and you have all summer for your trip. To get from L.A. to San Francisco you can choose to drive, fly, take a bus, or take the train. From San Francisco to Hawaii you can fly, cruise, or sail. In how many different ways can you travel from Los Angeles to Hawaii?

4. (2 pts) How many arrangements of the letters in the word SQUARE begin with SQ?

5. (2 pts) The volleyball team is sponsoring a mixed-doubles sand court volleyball tournament and sixteen pairs have signed up for the chance to win one of the seven trophies and cash prizes. In how many different ways can the teams be chosen and arranged for the top seven slots?

Answer 1

(2 pts)The probability that Sue will go to Mexico in the winter and to France in the summer is 0.40. The probability that she will go to Mexico in the winter is 0.60. Find the probability that she will go to France this summer given that she just returned from her winter vacation in Mexico.

This is conditional probability.

P(A given B) =

Event A: She goes to france in summer

Event B: She has gone to Mexico

Numerator: She has gone to Mexico and France

Therefore using the values we have

(2 pts ) A fair die is tossed. Find the probability P(less than 5|even).

Again it is conditional probability

Sample space of rolling a die = {1,2, 3, 4, 5, 6}

Event A : Less than 5 {1, 2, 3, 4} P(A) = 4/6

Event B : Even {2, 4, 6} P(B) = 3/6

= {2, 4} P = 2/6

P(A | B) =

( 2 pts) You have decided to take a vacation. You want to go from Los Angeles to San Francisco and then to Hawaii, and you have all summer for your trip. To get from L.A. to San Francisco you can choose to drive, fly, take a bus, or take the train. From San Francisco to Hawaii you can fly, cruise, or sail. In how many different ways can you travel from Los Angeles to Hawaii?

We have four options to choose from to go from LA to San Francisco. = 4

We have three options to choose from to go from SF to Hawaii = 3

The total ways in which one can go from LA to Hawaii= 4 * 3

The combinations can be drive and fly or drive and sail or bus and sail .....

(2 pts) How many arrangements of the letters in the word SQUARE begin with SQ?

There are six letters and six spaces. But letters SQ take two of the place and two letters are utilised. We are now left with 4 spaces and 4 letters. So we say that the 1st two blanks have one option. the rest as follows

3rd = 4

4th = 3

5th = 2

6th = 1

Therefore total ways it can be arranged are = 1 *4 * 3* 2*1

(2 pts) The volleyball team is sponsoring a mixed-doubles sand court volleyball tournament and sixteen pairs have signed up for the chance to win one of the seven trophies and cash prizes. In how many different ways can the teams be chosen and arranged for the top seven slots?

Thereare sixteen teams and 7 have to bechosen for the slot. Using the combination function we can get the number of ways since the arrangement is not important.

16C7 = 16! / (9! * 7!)