Question

You decide that you are going to flip a coin, and a six sided die.
What is the probability of the following events?
Tails and an even number? (Round to two decimal places)
Tails and the number 9?
Heads or a number bigger than 4? (Round to two decimal places)
Heads or the number 2? (Round to two decimal places)

Answer 1

Probability helps us to know the chances of an event occurring. The probability of getting a tail and an even number is 0.25.

What is Probability?

Probability helps us to know the chances of an event occurring.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

Since a coin has two faces, therefore, the probability of getting either of the sides of the coin is (1/2). While a die has six faces, so the probability of getting any side of the die is (1/6).

A.) The probability of getting a tail and an even number can be written as,

$\text{Probability of getting a tail} = \dfrac{1}{2}$

$\text{Probability of Even Number(2,4,6) } = \dfrac{3}{6} = \dfrac{1}{2}$

$\text{Probability (Tails and an even number)} = \dfrac12 \times \dfrac12 = 0.25$

B.) The Probability of getting tails and the number 9 can be written as,

$\text{Probability of getting a tail} = \dfrac{1}{2}$

$\text{Probability of Number 9} = \dfrac{0}{6} = 0$

$\text{Probability of the tails and the number 9} = 0$

C.) The Probability of getting Heads or a number bigger than 4 can be written as,

$\text{Probability of getting a Head} = \dfrac{1}{2}$

$\text{Probability of a number bigger than 4 (5,6) } = \dfrac{2}{6} = \dfrac{1}{3}$

$\text{Probability (Heads or a number bigger than 4 )} = \dfrac12 + \dfrac13 = \dfrac{5}{6} = 0.83333$

D.) The Probability of getting Heads or the number 2 can be written as,

$\text{Probability of getting a Head} = \dfrac{1}{2}$

$\text{Probability of the number 2} = \dfrac{1}{6}$

$\text{Probability (Heads or the number 2 )} = \dfrac12 + \dfrac16 = \dfrac{8}{12} = 0.6666$

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