Question

special deck of cards has 20 cards. Nine are green, seven are blue, and four are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? B. Let A be the event that a red card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number to 1 decimal place. C. Let B be the event that a green or blue is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? D. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?

Answer 1

Answer:

Step-by-step explanation:

Given that special deck of cards has 20 cards. Nine are green, seven are blue, and four are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin

A) Sample space will have Green, Head,  or Green, Tail .... Red, head, red, tail

No of elements in sample space = no of colours x no of outcomes in coin toss

= 4x2 = 8

B) A= getting (RT)

P(A) = Prob of getting red card and tail on coin

= P (R) *P(T)

=$\frac{4}{20} *\frac{1}{2} \\=\frac{1}{10}$

C) B be the event that a green or blue is picked, followed by landing a tail on the coin toss

B = getting green card and tail

Getting green card tail is mutally exclusive with red card and tail as there is no common element between green and blue.

D) C= red or green card is picked followed by tail.

Here A and C have a common element as getting red and tail.  So not mutually exclusive