Question

If Quinn tosses a fair coin and then rolls a fair number cube labeled 1 through 6, what is the probability of tossing heads followed by rolling a number less than 4?

Answer 1

(1/2)(3/6)=1/4

The probability of rolling a head (or tail for that matter is 1/2)

The probability of rolling less than 4 with a die is 3/6)

Thus the probability of both occurring is 1/4

Answer 2

Answer:  $\dfrac{1}{4}$

Step-by-step explanation:

Given : If Quinn tosses a fair coin and then rolls a fair number cube labeled 1 through 6.

Event 1 : Tossing heads

Event 2 : Rolling a number less than 4.

Total outcomes on tossing a coin [tails , heads]= 2

Probability of tossing heads : $P(E_1)=\dfrac{1}{2}$

Total outcomes on a fair number cube= 6

Number of outcomes less than 4 {1,2,3}=3

Probability of rolling a number less than 4 =$P(E_2)=\dfrac{3}{6}=\dfrac{1}{2}$

Since , both the events are independent events , then

The probability of tossing heads followed by rolling a number less than 4 :-

$P(E_1)\times P(E_2)=\dfrac{1}{2}\times\dfrac{1}{2}=\dfrac{1}{4}$

Hence, the probability of tossing heads followed by rolling a number less than 4 = $\dfrac{1}{4}$