Question

Suppose you flip a coin twice and count the number of heads you observe. You then roll a 4 sided die (like a 6 sided die, but only has values 1 through 4).

If the random variable Y is the number of heads you've observed multiplied by the vaule of your die roll, what is the sample space of Y?

What is the probability Y <1?

Answer 1

Y= {0, 0, 0, 0, 1, 2, 2, 3, 4, 4, 6, 8}

P (Y < 1) = 0.25 = 25%

Explanation:

The possible outcomes for the number of heads are 0, 1 or 2, while the possible outcomes for the dice roll are 1, 2, 3 or 4. The sample space for Y is:

0 x 1 =0; 0 x 2 = 0; 0 x 3=0; 0 x 4 =0;

1 x 1 =1; 1 x 2 = 2; 1 x 3=3; 1 x 4 =4;

2 x 1 =2; 2 x 2 = 4; 2 x 3=6; 2 x 4 =8;

Y= {0, 0, 0, 0, 1, 2, 2, 3, 4, 4, 6, 8}

For Y < 1, the number of heads must be zero, the probability of getting zero heads on two tosses is:

`P(Y<1) = (1)/(2)*(1)/(2)=0.25`