Child\'s game is played with cards that are marked with cartoon bunnies, cats, a

Question

Child's game is played with cards that are marked with cartoon bunnies, cats, and dogs. Each animal is either orange or blue. There are 7 blue and 3 orange bunnies, 9 blue and 5 orange cats, and 5 blue and 10 orange dogs. One card is chosen at random from the deck. Let A be the event that the card shows a cat and let B be the event that the card is orange. Consider the following events.

i. A B'

ii. A B

iii. A' B'

iv. (A'B)'

a.) For each of the events, write a statement (in words not set notation) that describes the event in terms of animals and colors.

b.) Find the probability of the event.

Explanation / Answer

total number of cards =7+3+9+5+5+10=39

(i)

a) AUB' =event that card is at least cat or not orange or both.

b) P(AUB') =(7+9+5+5)/39 =24/39 =8/13

(ii)

a)AnB =event that card is of cat as well of orange color

b)P(AnB) =5/39

(iii)

A' nB' =event that card belongs to neither of cat nor orange color

P(A' nB' ) =(7+5)/39=12/39=4/13

(iv) (A'nB)' =AUB' =

event that card is at least cat or not orange or both.

b) P(A'nB)' =P(AUB') =(7+9+5+5)/39 =24/39 =8/13

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