Math 237 HW and Practice Problems 1. Four cards are drawn without replacement fr

Question

Math 237 HW and Practice Problems 1. Four cards are drawn without replacement from a deck of 52 cards. What is thoe probability of obtaining at least one Ace or at least one Jack? 2. A committee of 5 is chosen from a group of 7 men and 5 women. What is the probability the group contains a majority of men? 3. A box contains tags numbered 1,2 n Two tags are chosen without replacement. What is the probability they are consecutive integens? 4. You ask your neighbor to water a sickly plant while you are on vacation. Without water, it will die with probability 8; with water, it will die with probability.15 You are 90 percent certain that your neighbor will remember to water the plant. a) What is the probability the plant will be alive upon your return? b) If the plant is dead upon your returm, what is the probability that your neighbor forgot to water it? 5. Given: A and B are events with P(A) 0.4, P(B)-0.6, and P(AUB)-.9. Find a) PAnB). b) P(BA) 6.(Extra Credit): Show that if E and F are independent then Ec and Fc are independent.

Explanation / Answer

1)

total ways of picking 4 cards is 52C4

ways in which atleast 1 ace can be calculated as 1- ways in which we dont get ace at all , there are 48 non aces in the deck , which can be picked in 48C4 ways

so req probability for ace is

1 - (48C4)/(52C4)

likewise

ways in which atleast 1 jack can be calculated as 1- ways in which we dont get jack at all , there are 48 non aces in the deck , which can be picked in 48C4 ways

so req probability for jack is

1 - (48C4)/(52C4)

so as this is an OR

we add the 2 probabilites as

2*(1 - (48C4)/(52C4))

2*(1- 194580/270725)

= 0.5625

Please note that we can answer only 1 question at a time , as per the answering guidelines

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