Question

an unbiased die is thrown. what is the probability of getting a). a number less than 5 divisible by 2. b). a number greater than 2 divisible by 3. c). an even number or a multiple of 3. d). an even number and a multiple of 3 e). a number 3 or 4. f). a number between 3 and 6​

Answer 1

Answer:

a. 1/3

b. 1/3

c. 1/2

d. 1/6

e. 1/3

f. 1/3

I hope it helps you ☺☺

Answer 2

Given:

Given that an unbiased die is thrown.

To Find:

We have to find out the following.

a) A number that is divisible by two and is less than five.

b). A number greater than 2 is divisible by 3.

c). An even number or a multiple of 3.

d). An even number and a multiple of 3.

e). A number either 3 or 4.

f). A number between 3 and 6.

Solution:

The numbers obtained in a single throw of dice = 1, 2, 3, 4, 5 or 6.

∴, Total number of outcomes = 6.

$Probability = \frac{Total number of outcomes}{Favorable number of outcomes}.$

a). The numbers that are divisible by two and are less than five = 1, 2, 3, 4.

Favorable number of outcomes = 4.

P (numbers that are divisible by two and are less than five) = $\frac{4}{6} = \frac{2}{3}.$

b). The numbers that are greater than 2 and is divisible by 3 = 3, 6.

Favorable number of outcomes = 2.

P (numbers that are greater than 2 and is divisible by 3) = $\frac{2}{6} = \frac{1}{3}.$

c). The numbers that are even or a multiple of 3 = 2, 3, 4, 6.

Favorable number of outcomes = 4.

P (numbers that are even or a multiple of 3) = $\frac{4}{6} = \frac{2}{3}.$

d). The numbers that are even and a multiple of 3 = 6.

Favorable number of outcomes = 1.

P (numbers that are even and a multiple of 3) = $\frac{1}{6}.$

e). The numbers that is either 3 or 4 = 3, 4.

Favorable number of outcomes = 2.

P (numbers that is either 3 or 4) = $\frac{2}{6} = \frac{1}{3}.$

f). The numbers between 3 and 6​ = 4, 5.

Favorable number of outcomes = 2.

P (numbers between 3 and 6) = $\frac{2}{6} = \frac{1}{3}.$

Hence, the probability of the given situations, a, b, c, d, e, and f are $\frac{2}{3}, \frac{1}{3}, \frac{2}{3}, \frac{1}{6}, \frac{1}{3}, and \frac{1}{3}$ , respectively.

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